Many-body localization edge in the random-field Heisenberg chain
Alet, Fabien (CNRS, Laboratoire de Physique Theorique, Université Paul Sabatier, Toulouse, France) |
We present our recent large scale exact diagonalization study [1] of the one dimensional spin 1/2 Heisenberg model in a random magnetic field. In order to access properties at varying energy densities across the entire spectrum for system sizes up to L=22 spins, we use a spectral transformation which can be applied in a massively parallel fashion. Our results allow for an energy-resolved interpretation of the many body localization transition including the existence of an extensive many-body mobility edge. The ergodic phase is well characterized by Gaussian orthogonal ensemble statistics, volume-law entanglement, and a full delocalization in the Hilbert space. Conversely, the localized regime displays Poisson statistics, area-law entanglement and non ergodicity in the Hilbert space where a true localization never occurs. We perform finite size scaling to extract the critical edge and exponent of the localization length divergence.
[1] David J. Luitz and Nicolas Laflorencie and Fabien Alet, arXiv:1411.0660 |
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Dynamical energy transfer in ac driven quantum systems
Arrachea, Liliana (Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, Buenos Aires, Argentina) |
Liliana Arrachea in collaboration with Maria Florencia Ludovico, Jong Soo Lim, Michael Moskalets and David Sanchez
We analyze the time-dependent energy and heat flows in a quantum system coupled to a fermionic continuum. The system is periodically forced with an external power source that supplies energy into the system. On the basis of a tunneling Hamiltonian, which is exactly solved by recourse to non-equilibirum Green functions and scattering theory, we discuss the different contributions to the total energy flux. We then derive the appropriate expression for the dynamical dissipation, in accordance with the fundamental principles of thermodynamics. Remarkably, we find that the dissipated heat can be expressed as a Joule law with a universal resistance that is constant at all times. |
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Many body localization of particles coupled to a 1d random harmonic lattice
Banerjee, Sumilan (Weizmann Institute of Science, Weizmann Institute of Science, Department of Condensed Matter Physics, Rehovot, Israel) |
Sumilan Banerjee and Ehud Altman
Department of Condensed Matter Physics, Weizmann Institute of Science
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We discuss the possibility to realize a many-body localized state of particles coupled to gapless and asymptotically delocalized phonons. This is in contrast to the general belief that such coupling to phonons would inevitably lead to delocalization through phonon assisted tunneling. Specifically we consider a system of electrons coupled to a 1d random harmonic chain and analyze the phonon-mediated hopping transport for both weak and strong coupling regimes. We also comment on implications of our approach for higher dimensional electron-phonon systems. |
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From non-equilibrium to perfectly adiabatic dynamics across the critical point
Damski, Bogdan (Jagellonian University, Institute of Physics, Krakow, Poland) |
A quantum system driven across the critical point undergoes non-equilibrium dynamics due to disappearence of the gap in its excitation spectrum. The key features of such dynamics are captured by the Kibble-Zurek theory, which predicts creation of topological defects during dynamical (symmetry-breaking) quantum phase transitions. We will discuss the probability of finding the system in the ground state after the dynamical crossing of the critical point.
First, we will show how knowledge of the ground state fidelity --i.e., the overlap between different ground states of the system -- can be used to explain the exponential dependence of the probability of ground state preparation on the system size. We will also show how this probability depends on the critical exponents of the system. Therefore, we will show the connection between the popular fidelity approach to quantum phase transitions and the field of the dynamics of quantum phase transitions.
Second, we will discuss how the adiabatic dynamics across the critical point can be strickly enforced by a proper modification of the Hamiltonian of the system. We will focus on the quantum Ising model and discuss the exact form of the so-called counterdiabatic modification of the Hamiltonian that achieves this goal. We will also discuss various approximations leading to nearly perfect suppression of the system excitaton in the quantum critical region and explain their infeficiency by the enhancement of the finite-size effects by quantum criticality. |
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Strongly correlated phases and ferromagnetic phases of fermions in an optical flux lattice model
Davenport, Simon (University of Cambridge, Theory of Condensed Matter (TCM), Cavendish Laboratory, Cambridge, United Kingdom) |
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Non-equilibrium dynamics across a localization-delocalization transition
Divakaran, Uma (Indian Institute of Technology Kanpur, Physics, Kanpur, India) |
The non-equilibrium dynamics of one-dimensional $XX$-model in a quasi-periodic transverse-field described by the Harper potential is studied. It is known that for weak transverse field, $hh_c$.
The non-equilibrium relaxation of the system is studied by applying two protocols:
a sudden change of $h$ (quench dynamics)
and a slow change of $h$ in time (adiabatic dynamics).
For a quench into the delocalized (localized) phase,
the entanglement entropy grows linearly (saturates)
and the order parameter decreases exponentially
(has a finite limiting value). For a critical quench the entropy
increases algebraically with time, whereas the order parameter
decreases with a stretched-exponential. The density of defects after an
adiabatic field change through the critical point is shown to scale with a power of the rate of field change. |
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Arctic circle phenomena as imaginary time light-cone effects
Dubail, Jerome (CNRS, Institut Jean Lamour, Statistical physics group, Vandoeuvre les Nancy, France) |
A similarity between light-cone effects in quantum spin chains and arctic-circle phenomena in classical statistical mechanics models, such as dimer models or six-vertex models, is noted. In the particular case of the XX chain, an explicit calculation shows that when the system is released from an initial "domain-wall state", with polarized spin $dots uparrow uparrow uparrow uparrow uparrow uparrow uparrow downarrow downarrow downarrow downarrow downarrow downarrow downarrow dots$, then its imaginary-time dynamics gives rise to a spatial separation between fluctuating and frozen regions, and that the fluctuating region is exactly circular, like in dimer models. |
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Quenching dynamics of a p-wave superconducting chain
Dutta, Amit (Indian Institute of Technology Kanpur, Department of Physics, Kanpur, India) |
We address the question of the fate of an edge Majorana under a sudden quenching
or slow ramping of one of the parameters of the $p$-wave superconducting Hamiltonian. We show that when the chain is suddenly quenched from one topological phase to the critical line separating the other topological phase, there is an interesting collapse and revival pattern of the edge Majorana. Earlier studies established that an edge Majorana can not be adiabtically trasported from one topological phase to the other under a slow quenching. Considering a generalized p-wave chain, where effective time reversal symmetry is broken leading to an extended gapless region separating two topological phases, we show that, remarkably, there exists a finite probability of an adiabatic transport of the edge Majorana from one topological phase to the other. This happens for an optimum transit time of the Majorana through the gapless phase, that is proportional to the system size and diverges for a thermodynamically large chain. |
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Odd Bose condensation in steady states far from equilibrium
Eckardt, Andre (Max-Planck Institute for the Physics of Complex Systems (MPIPKS), Dresden, Germany) |
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Competing energy scales in the renormalization group flow of quantum dot setups with periodically varying parameters
Eissing, Katharina (RWTH Aachen University, Institut für Theorie der statistischen Physik, Aachen, Germany) |
The functional renormalization group (fRG) has proven to be a versatile tool to investigate correlated, low-dimensional systems in and out of equilibrium. It was recently extended to study quantum dot setups with explicitly time dependent Hamiltonians [Phys. Rev. B 85, 085113 (2012)]. In systems in which one or more of the dot or lead parameters are varied periodically in time a periodic steady state is reached after all transients have died out. However, due to the limited simulation time the physics of this state can only be described, if we take advantage of the periodicity by combining the Floquet theorem and set up a functional RG with Green functions written in the Floquet basis. For the interacting resonant level model which in equilibrium and if driven by a time constant bias voltage is characterized by power-law scaling of observables in the relevant energy scales (e.g. temperature $T$ or bias voltage $V_b$, respectively) with interaction dependent exponents this allows to investigate if and how the driving frequency $Omega$ acts as a cutoff of the underlying renormalization group flow. The competition of this scale with the emergent low-energy scale $T_K$ (Kondo scale) is investigated. I discuss how this competition is reflected in the observables characterizing the stationary transport through the dot. |
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Purification and many-body localization in cold atomic gases
Enss, Tilman (Universität Heidelberg, Institut für Theoretische Physik, Heidelberg, Germany) |
We propose to observe many-body localization in cold atomic gases by realizing a Bose-Hubbard chain with binary disorder and studying its nonequilibrium dynamics. In particular, we show that measuring the difference in occupation between even and odd sites, starting from a prepared density-wave state, provides clear signatures of localization. Furthermore, we confirm as hallmarks of the many-body localized phase a logarithmic increase of the entanglement entropy in time and Poissonian level statistics. Our numerical density-matrix renormalization group calculations for infinite system size are based on a purification approach; this allows us to perform the disorder average exactly, thus producing data without any statistical noise and with maximal simulation times of up to a factor 10 longer than in the clean case. |
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Linking dynamic and static features of many-body localisation
Friesdorf, Mathis (FU Berlin, Department of physics, Berlin, Germany) |
Generic interacting many-body systems are usually expected to thermalise following out of equilibrium dynamics: Local expectation values should be captured in terms of thermal ensembles. A notable class of models that contradicts this intuition is given by systems exhibiting many-body localisation (MBL). Their eigenstates are strongly lacking entanglement, concomitant with an absence of thermalisation, while their dynamical evolution is characterised by a strong suppression of transport, the existence of local constants of motion and slow entanglement growth.
We present a general overview of the dynamic and static features of MBL. Based on two recent preprints (http://arxiv.org/abs/1409.1252,http://arxiv.or/abs/1412.5605), we proceed to link those different aspects of MBL. In particular, we rigorously prove that, quite counterintuitively, the existence of a
single constant of motion is sufficient to guarantee information propagation. Our work constitutes an important clarifying step towards a comprehensive and unified definition of MBL.
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Renormalization group approach to the polaron problem in and out-of equilibrium
Grusdt, Fabian (University of Kaiserslautern, Department of Physics, Germany) |
We developed a renormalization group approach for analyzing Fröhlich polarons, which we apply to a problem of impurity atoms immersed in a Bose-Einstein condensate of ultra cold atoms. Polaron energies obtained by our method are in excellent agreement with recent diagrammatic Monte Carlo calculations for a wide range of interaction strengths. We generalize our approach to solve non-equilibrium polaron problems, for example the dynamics of polaron formation after a sudden quench of the interactions. Possible experimental tests of our results in current experiments with ultra cold atoms are discussed. |
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Propagation dynamics in Heisenberg spin chains and ladders
Haque, Masudul (Max Planck Institute for Physics of Complex Systems, Condensed Matter, Dresden, Germany) |
I present some non-equilibrium phenomena in the anisotropic Heisenberg
(XXZ) chain and in the Heisenberg spin ladder, involving scattering, correlated propagation of bound multi-magnons, and localization.
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Slowest local operators in quantum spin chains
Kim, Hyungwon (Rutgers University, Physics, Piscataway, USA) |
We numerically construct slowly relaxing local operators in a nonintegrable spin-1/2 chain. Restricting the support of the operator to M consecutive spins along the chain, we exhaustively search for the operator that minimizes the Frobenius norm of the commutator with the Hamiltonian and show that the Frobenius norm bounds the time scale of relaxation of the operator. We find operators with significantly slower relaxation than the slowest simple "hydrodynamic" mode due to energy diffusion. Using both exhaustive search and tensor network techniques, we find similar slowly relaxing operators for a Floquet spin chain and for quantum circuits on spin chains; these systems are hydrodynamically "trivial", with no conservation laws restricting their dynamics. We argue that such slow relaxation may be a generic feature following from locality and unitarity. |
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Dynamical Spin Correlations in (non-)Abelian Kitaev Spin Liquids. Bound States and the Role of Disorder
Knolle, Johannes (University of Cambridge, Cavendish Laboratory, TCM Group, Cambridge, United Kingdom) |
We study the dynamical spin response of (non-)Abelian quantum spin liquids (QSLs) in Kitaev’s honeycomb model. The structure factor shows clear signatures of fractionalization, a key feature of topologically ordered states, in the gapless and gapped Kitaev QSL phases. We find that remarkably, apart from a broad continuum, which is expected for a fractionalized system, sharp features can show up in a dynamical response due to the presence of quasiparticle bound states. In the anisotropic gapped Abelian QSL a gauge flux excitation leads to a delta-functional response in one of the spin components of the structure factor. In contrast, in the isotropic non-Abelian QSL (with broken time reversal symmetry) sharp features appear in all three components, that can be traced back to a localized composite fermion-flux bound state which is a hallmark signature of the non-Abelian phase. We find that these features in the response are surprisingly robust with respect to the addition of bond disorder. |
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Dynamic trapping near a quantum critical point
Kolodrubetz, Michael (Boston University, College of Arts and Sciences, Department of Physics, Boston, USA) |
The study of dynamics in closed quantum systems has recently been revitalized by the emergence of experimental systems that are well-isolated from their environment. In this talk, I consider the closed-system dynamics of an archetypal model: spins near a second order quantum critical point, which are traditionally described by the Kibble-Zurek mechanism. Imbuing the driving field with Newtonian dynamics, I find that the full closed system exhibits a robust new phenomenon -- dynamic critical trapping -- in which the system is self-trapped near the critical point due to efficient absorption of field kinetic energy by heating the quantum spins. I quantify limits in which this phenomenon can be observed and generalize these results by developing a Kibble-Zurek scaling theory that incorporates the dynamic field. I show that similar phenomena can be seen in classical or thermal systems. These findings can also potentially be interesting in the context of early universe physics, where the role of the driving field is played by the inflaton or a modulus. |
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Dynamical response in an exactly solvable model of a quantum spin-liquid
Kovrizhin, Dmitry (University of Cambridge, Cavendish Laboratory, TCM, Cambridge, United Kingdom) |
I will present the theory of a dynamical response, and the
results for the dynamic structure factor (SF) in the two-dimensional
exactly solvable model of a quantum spin-liquid (Kitaev model),
and its 3D generalisation. Remarkably, we obtain a novel dynamical
phase diagram, and find that the spin-response shows the
signatures of fractionalized excitations (Majorana fermions). |
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Many-body mobility edge due to symmetry-constrained dynamics and strong interactions
Mondragon, Ian (University of Illinois at Urbana-Champaign, Institute of Condensed Matter Theory (ICMT), Physics, Urbana, USA) |
We provide numerical evidence combined with an analytical understanding of the many-body mobility edge for the strongly anisotropic spin-1/2 XXZ model in a random magnetic field. The system dynamics can be understood in terms of symmetry-constrained excitations about parent states with ferromagnetic and anti-ferromagnetic short range order. These two regimes yield vastly different dynamics producing an observable, tunable many-body mobility edge. We compute a set of diagnostic quantities that verify the presence of the mobility edge and discuss how weakly correlated disorder can tune the mobility edge further. |
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Superfluid-insulator transition of interacting bosons in one dimension
Petkovic, Aleksandra (University Paul Sabatier, Toulouse III, LPT Toulouse, Physics, Toulouse, France) |
We consider one-dimensional system of interacting bosons in a random potential. At zero temperature, it can be either in the superfluid or in the insulating phase. We study the transition using bosonization and renormalization group method, derive the two-loop scaling equations and discuss the phase diagram. We find that the correlation functions at the transition are characterized by universal exponents in a finite region around the fixed point. We also study a disordered two-leg bosonic ladder with correlated disorder across the rung . The latter system exhibits a transition between the superfluid and disordered phase where the exponents of correlation functions do not take universal values. |
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Localized system coupled to small baths: From Anderson to Zeno
Pietracaprina, Francesca (SISSA - International School for Advanced Studies, Statistical Physics, Trieste, Italy) |
We investigate what happens if an Anderson localized system is coupled to a small delocalized bath. We find that the effect of the bath on localization in the system is a non-monotonic function of the coupling between system and bath. At weak couplings, the bath facilitates transport by allowing the system to 'borrow' energy from the bath, while above a certain coupling the bath produces localization; we call this last regime the regime of "Zeno-localization", since the physics of this regime is akin to the quantum Zeno effect, where frequent measurements of the position of a particle impede its motion. We confirm our results by numerical exact diagonalization. |
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Correlations in non-equilibrium Luttinger liquids and singular Fredholm determinants.
Protopopov, Ivan (Karlsruhe Institute of Technology, Institut für Theorie der Kondensierten Materie, Karlsruhe, Germany) |
We study interaction-induced correlations in non-equilibrium Luttinger liquid with multiple Fermi edges. Many-particle correlation functions are expressed in terms of Fredholm determinants $det(1 + AB)$, where A(epsilon) and B(t) have multiple discontinuities in energy and time spaces. We propose a general asymptotic formula for this class of determinants and provide analytical and numerical support to this conjecture. This allows us to establish nonequilibrium Fermi-edge singularities of many-particle correlation functions. As an example, we calculate a two-particle distribution function characterizing genuinely nonequilibrium quantum correlations between left- and right-moving fermions that have left the interaction region. |
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Decay of excitations in interacting one-dimensional Bose gases
Ristivojevic, Zoran (Ecole Polytechnique, Center for Theoretical Physics, Palaiseau, France) |
Excitation spectrum in weakly-interacting systems of bosons have
the Bogoliubov form. In three dimensions, those excitations are
unstable due to residual weak interactions. The resulting process
is known as Beliaev decay [1,2] and has been experimentally
observed [3]. The related problem of decay of excitations in
one-dimensional Bose gases is a fundamental long-standing
problem. In this talk I will present its solution [4]. As a result of
the conservation laws in one dimension, at zero temperature the
leading mechanism of decay of a quasiparticle excitation is its
disintegration into three others. We find that a phonon excitation
has a decay rate proportional to the seventh power of momentum.
In the integrable case of contact interaction between the bosons,
the decay rate vanishes. Our theory is based on studying the
anharmonic effects produced by the leading integrability breaking
perturbations to the Lieb-Liniger model. It is not limited to the
decay of lowest momentum phonon excitations and can describe
full crossover as momentum increases and the excitation
spectrum approaches its quadratic form.
[1] S. T. Beliaev, Sov. Phys. JETP 7, 299 (1958).
[2] L. D. Landau and E. M. Lifshitz, Statistical Physics, Part 2
(Pergamon Press, Oxford, 1980).
[3] N. Katz, J. Steinhauer, R. Ozeri, and N. Davidson, Phys. Rev.
Lett. 89, 220401 (2002).
[4] Z. Ristivojevic and K. A. Matveev, Phys. Rev. B 89, 180507(R) (2014). |
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Integrals of motion in the Many Body localized phase
Ros, Valentina (SISSA - International School of Advanced Studies, Trieste, Italy) |
We construct a complete set of quasi-local integrals of motion for the many-body localized phase of interacting fermions in a disordered potential. The integrals of motion can be chosen to have binary spectrum {0,1}, thus constituting exact quasiparticle occupation number operators for the Fermi insulator. We map the problem onto a non-Hermitian hopping problem on a lattice in operator space. We show how the integrals of motion can be built, under certain approximations, as a convergent series in the interaction strength. An estimate of its radius of convergence is given, which also provides an estimate for the many-body localization-delocalization transition. Finally, we discuss how the properties of the operator expansion for the integrals of motion imply the presence or absence of a finite temperature transition.
AUTHORS: V.Ros, M.Mueller, A.Scardicchio
REFERENCE: Nuclear Physics B 891 (2015) 420-465 |
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Dynamics in many-body localized quantum systems without disorder
Schiulaz, Mauro (International School for Advanced Studies, SISSA/ISAS, Trieste, Italy) |
We study the relaxation dynamics of strongly interacting quantum systems that display a kind of
many-body localization despite of their translation invariant Hamiltonian. We show that dynamics
starting from a random initial conguration are non-perturbatively slow in the hopping
strength, and potentially genuinely non-ergodic in the thermodynamic limit. In nite
systems with periodic boundary conditions, relaxation takes place in two stages, separated by a long
out-of-equilibrium plateau whose duration diverges exponentially with system size. We estimate the
phase boundary of this quantum glass phase, and discuss the role of local resonant congurations.
Experimental realizations are suggested. |
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Anomalously long-range order in one dimensional Bose gases far from equilibrium
Schnell, Alexander (Max-Planck-Gesellschaft, Max-Planck-Institut für Physik komplexer Systeme, Quantum Chaos and Quantum Dynamics, Dresden, Germany) |
We study non-equilibrium steady states
in driven-dissipative systems, where
the notion of a ground state may become meaningless.
In ideal Bose gases far from thermodynamic equilibrium, Bose-Einstein condensation generalises to the
selection of a group of single-particle states acquiring almost all particles in the limit of large particle densities, while the
occupations of all other states saturate [1].
Surprisingly, driving a finite one-dimensional
system into non-equilibrium can increase
particle coherences by orders of magnitude:
We couple a tight-binding chain to a heat bath
with temperature~$T$ and a second, population
inverted bath, with temperature~$-T$.
In this non-equilibrium setting,
we find fragmented Bose-Einstein condensation and long-range particle coherences at particle densities~$n$ where there is no condensation in
equilibrium at temperature~$T$.
At fixed particle density~$n$ and bath temperature~$T$, we are able
to retain this fragmented condensation even as the chain becomes infinitely long by a sophisticated choice of the coupling to the baths.\
noindent [1] Vorberg et.~al., Phys. Rev. Lett. 111, 240405 |
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Thermal pure quantum state and its dynamical behavior
Sugiura, Sho (University of Tokyo, Department of Physics, Japan) |
A thermal equilibrium state of a quantum many-body system can be represented
by a typical pure quantum state, which we call a thermal pure quantum (TPQ) state.
We have found the microcanonical TPQ state, which give the same thermodynamicpredictions
as the microcanonical ensemble gives [1], and the canonical TPQ state,which give
the predictions same as the canonical ensemble [2]. The TPQ states corresponding
to other ensembles can also be constructed [3]. We have thus established the TPQ
formulation of statistical mechanics, according to which all quantities of
statistical-mechanical interest are obtained from a single realization of either TPQ state.
In this talk, we focus on dynamical quantities. We will show that dynamical
correlations are also given by a single realization of TPQ state. Namely, their values
converge in probability to the correct result. Thus, we can obtain the result of
Green-Kubo formula from a single realization of TPQ state.
[1] S. Sugiura and A. Shimizu, "Thermal Pure Quantum States at Finite Temperature",
Phys. Rev. Lett. 108, 240401 (2012).
[2] S. Sugiura and A. Shimizu, "Canonical Thermal Pure Quantum State",
Phys. Rev. Lett. 111, 010401 (2013).
[3] M. Hyuga, S. Sugiura, K. Sakai, and A. Shimizu, "Thermal Pure Quantum States
of Many-Particle Systems", Phys. Rev. B 90, 121110(R) (2014).
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Bose-Hubbard ladder subject to effective magnetic field: geometry and dynamics
Tschischik, Wladimir (Max Planck Institute for the Physics of Complex Systems, Condensed Matter Department, Dresden, Germany) |
Motivated by a recent experimental realization of an optical lattice system with an effective magnetic field (Atala et al., Nature Physics 10, 588 (2014)), we study a Bose-Hubbard system on a two-leg ladder with complex hopping amplitudes. This system shows a quantum phase transition already without interactions. We examine and present differences between the periodic, open-boundary, and harmonically trapped cases. We present a striking "slowing down" effect in the collective mode dynamics near the phase transition. |
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Semiclassical theory of fidelity decay and coherent echoes in interacting many-body quantum systems
Urbina, Juan-Diego (Initute for Theoretical Physics, Complex Quantum Systems, Regensburg, Germany) |
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Topological classification of dynamical phase transitions
Vajna, Szabolcs (Budapest University of Technology and Economics (BUTE), Institute of Physics, Department of Physics, Budapest, Hungary) |
We study the time evolution of a variety of one and two dimensional systems (including SSH model, Kitaev-chain, Haldane model, p+ip superconductor, etc.) following a sudden quench. We prove analitically that topology-changing quenches are always followed by non-analytic temporal behaviour of return rates (logarithm of the Loschmidt echo), refered to as dynamical phase transitions (DPTs). Similarly to edge states in topological insulators, DPTs can be classified as being topologically protected or not.
In 1D systems the number of topologically protected non-equilibrium time scales are determined by the difference between the initial and final winding numbers, while in 2D no such relation exists for the Chern numbers.
The singularities of the return rates in the 2D case are qualitatively different from those of the 1D case, the cusps appear only in the first time derivative. |
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Nonsmooth and level-resolved dynamics illustrated with a periodically driven tight-binding model
Zhang, Jiang-min (Max-Planck-Institut für Physik komplexer Systeme, Condensed matter (Masudul Haque), ) |
We point out that in the first order time-dependent perturbation theory, the transition probability may behave nonsmoothly in time and have kinks periodically. Moreover, the detailed temporal evolution can be sensitive to the exact locations of the eigenvalues in the continuum spectrum, in contrast to coarse-graining ideas. Underlying this nonsmooth and level-resolved dynamics is a simple equality about the sinc function sinc x = sin x/x. These physical effects appear in many systems with approximately equally spaced spectra, and is also robust for larger-amplitude coupling beyond the domain of perturbation theory. We use a one-dimensional periodically driven tight-binding model to illustrate these effects, both within and outside the perturbative regime. |
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Laser driven one dimensional quantum magnet
Zotos, Xenophon (University of Crete, Cretan Center for Quantum Complexity and Nanotechnology, Physics Department, Heraklion - Crete, Greece) |
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