Research areas

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In the Condensed Matter Division we are interested in a broad range of collective phenomena. These can be grouped under three central umbrellas of quantum matter, new kinds of order and quantum dynamics, while still substantial interconnections naturally emerge, see the illustration in the figure above.

A key scope of research is the identification and theoretical description of new kinds of order ranging from unconventional phases such as quantum spin liquids appearing in frustrated magnets to topological matter. These phases often cannot be described by local order parameters but rather entail peculiar entanglement properties linking condensed matter theory directly to quantum information concepts.

The far from equilibrium regime on the other hand, nowadays experimentally accessible in so-called quantum simulators, naturally provides the room for novel quantum states because constraints by equilibrium principles such as the equal a priori probability in the microcanonical ensemble are lifted generically. Prominent examples include the many-body localized phase or eigenstate phases in periodically driven Floquet systems such as discrete time crystals. Detailed descriptions of the individual research topics can be found under the respective embedded links in the figure above.



Avoided quasiparticle decay from strong quantum interactions
Ruben Verresen, Roderich Moessner, Frank Pollmann

Quantum states of matter-such as solids, magnets and topological phases-typically exhibit collective excitations (for example, phonons, magnons and anyons)1. These involve the motion of many particles in the system, yet, remarkably, act like a single emergent entity-a quasiparticle. Known to be long lived at the lowest energies, quasiparticles are expected to become unstable when encountering the inevitable continuum of many-particle excited states at high energies, where decay is kinematically allowed. Although this is correct for weak interactions, we show that strong interactions generically stabilize quasiparticles by pushing them out of the continuum. This general mechanism is straightforwardly illustrated in an exactly solvable model. Using state-of-the-art numerics, we find it at work in the spin- 1/2 triangular-lattice Heisenberg antiferromagnet (TLHAF). This is surprising given the expectation of magnon decay in this paradigmatic frustrated magnet. Turning to existing experimental data, we identify the detailed phenomenology of avoided decay in the TLHAF material2 Ba3CoSb2O9, and even in liquid helium3,4,5,6,7,8, one of the earliest instances of quasiparticle decay9. Our work unifies various phenomena above the universal low-energy regime in a comprehensive description. This broadens our window of understanding of many- body excitations, and provides a new perspective for controlling and stabilizing quantum matter in the strongly interacting regime.

Nature Physics (2019)




Quantum localization bounds Trotter errors in digital quantum simulation
Markus Heyl, Philipp Hauke, and Peter Zoller

A fundamental challenge in digital quantum simulation (DQS) is the control of an inherent error, which appears when discretizing the time evolution of a quantum many-body system as a sequence of quantum gates, called Trotterization. Here, we show that quantum localization- by constraining the time evolution through quantum interference-strongly bounds these errors for local observables, leading to an error independent of system size and simulation time. DQS is thus intrinsically much more robust than suggested by known error bounds on the global many-body wave function. This robustness is characterized by a sharp threshold as a function of the Trotter step size, which separates a localized region with controllable Trotter errors from a quantum chaotic regime. Our findings show that DQS with comparatively large Trotter steps can retain controlled errors for local observables. It is thus possible to reduce the number of gate operations required to represent the desired time evolution faithfully.

Sci. Adv. 5, eaau8342 (2019)





Topological superconductivity in a phase-controlled Josephson junction
H. Ren, F. Pientka, S. Hart, A. T. Pierce, M. Kosowsky, L. Lunczer, R. Schlereth, B. Scharf, E. M. Hankiewicz, L. W. Molenkamp, B. I. Halperin, and A. Yacoby

Topological superconductors can support localized Majorana states at their boundaries1,2,3,4,5. These quasi-particle excitations obey non-Abelian statistics that can be used to encode and manipulate quantum information in a topologically protected manner6,7. Although signatures of Majorana bound states have been observed in one-dimensional systems, there is an ongoing effort to find alternative platforms that do not require fine-tuning of parameters and can be easily scaled to large numbers of states8,9,10,11,12,13,14,15,16,17,18,19,20,21. Here we present an experimental approach towards a two-dimensional architecture of Majorana bound states. Using a Josephson junction made of a HgTe quantum well coupled to thin-film aluminium, we are able to tune the transition between a trivial and a topological superconducting state by controlling the phase difference across the junction and applying an in-plane magnetic field22. We determine the topological state of the resulting superconductor by measuring the tunnelling conductance at the edge of the junction. At low magnetic fields, we observe a minimum in the tunnelling spectra near zero bias, consistent with a trivial superconductor. However, as the magnetic field increases, the tunnelling conductance develops a zero-bias peak, which persists over a range of phase differences that expands systematically with increasing magnetic field. Our observations are consistent with theoretical predictions for this system and with full quantum mechanical numerical simulations performed on model systems with similar dimensions and parameters. Our work establishes this system as a promising platform for realizing topological superconductivity and for creating and manipulating Majorana modes and probing topological superconducting phases in two-dimensional systems.

Nature 569, 93 (2019)




Accessing eigenstate spin-glass order from reduced density matrices
Younes Javanmard, Soumya Bera, and Markus Heyl

Many-body localized phases may not only be characterized by their ergodicity breaking, but can also host ordered phases such as the many-body localized spin-glass (MBL-SG). The MBL- SG is challenging to access in a dynamical measurement and therefore experimentally since the conventionally used Edwards-Anderson order parameter is a two-point correlation function in time. In this work, we show that many-body localized spin-glass order can also be detected from two-site reduced density matrices, which we use to construct an eigenstate spin-glass order parameter. We find that this eigenstate spin-glass order parameter captures spin-glass phases in random Ising chains both in many-body eigenstates as well as in the nonequilibrium dynamics from a local in time measurement. We discuss how our results can be used to observe MBL-SG order within current experiments in Rydberg atoms and trapped ion systems.

Phys. Rev. B 99, 144201 (2019)





Dynamical Structure Factor of the Three-Dimensional Quantum Spin Liquid Candidate NaCaNi2F7
S. Zhang, H. J. Changlani, K. W. Plumb, O. Tchernyshyov, and R. Moessner

We study the dynamical structure factor of the spin-1 pyrochlore material NaCaNi2F7, which is well described by a weakly perturbed nearest-neighbour Heisenberg Hamiltonian, Our three approaches-molecular dynamics simulations, stochastic dynamical theory, and linear spin wave theory-reproduce remarkably well the momentum dependence of the experimental inelastic neutron scattering intensity as well as its energy dependence with the exception of the lowest energies. We discuss two surprising aspects and their implications for quantum spin liquids in general: the complete lack of sharp quasiparticle excitations in momentum space and the success of the linear spin wave theory in a regime where it would be expected to fail for several reasons.

Phys. Rev. Lett. 122, 167203 (2019)




Correlation-induced localization
P. A. Nosov, I. M. Khaymovich, and V. E. Kravtsov

A new paradigm of Anderson localization caused by correlations in the long-range hopping along with uncorrelated on-site disorder is considered which requires a more precise formulation of the basic localization-delocalization principles. A new class of random Hamiltonians with translation- invariant hopping integrals is suggested and the localization properties of such models are established both in the coordinate and in the momentum spaces alongside with the corresponding level statistics. Duality of translation-invariant models in the momentum and coordinate space is uncovered and exploited to find a full localization-delocalization phase diagram for such models. The crucial role of the spectral properties of hopping matrix is established and a new matrix inversion trick is suggested to generate a one-parameter family of equivalent localization- delocalization problems. Optimization over the free parameter in such a transformation together with the localization-delocalization principles allows us to establish exact bounds for the localized and ergodic states in long-range hopping models. When applied to the random matrix models with deterministic power-law hopping this transformation allows to confirm localization of states at all values of the exponent in power-law hopping and to prove analytically the symmetry of the exponent in the power-law localized wave functions.

Phys. Rev. B 99, 104203 (2019)