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.



Quantum Many-Body Dynamics in Two Dimensions with Artificial Neural Networks
Markus Schmitt and Markus Heyl

The efficient numerical simulation of nonequilibrium real-time evolution in isolated quantum matter constitutes a key challenge for current computational methods. This holds in particular in the regime of two spatial dimensions, whose experimental exploration is currently pursued with strong efforts in quantum simulators. In this work we present a versatile and efficient machine learning inspired approach based on a recently introduced artificial neural network encoding of quantum many-body wave functions. We identify and resolve key challenges for the simulation of time evolution, which previously imposed significant limitations on the accurate description of large systems and long-time dynamics. As a concrete example, we study the dynamics of the paradigmatic two-dimensional transverse-field Ising model, as recently also realized experimentally in systems of Rydberg atoms. Calculating the nonequilibrium real-time evolution across a broad range of parameters, we, for instance, observe collapse and revival oscillations of ferromagnetic order and demonstrate that the reached timescales are comparable to or exceed the capabilities of state-of-the-art tensor network methods.

Phys. Rev. Lett. 125, 100503 (2020)




Multifractality Meets Entanglement: Relation for Nonergodic Extended States
Giuseppe De Tomasi and Ivan M. Khaymovich

In this work, we establish a relation between entanglement entropy and fractal dimension D of generic many-body wave functions, by generalizing the result of Page [Phys. Rev. Lett. 71, 1291 (1993)] to the case of sparse random pure states (SRPS). These SRPS living in a Hilbert space of size N are defined as normalized vectors with only N D (0 ≤ D ≤ 1) random nonzero elements. For D = 1, these states used by Page represent ergodic states at an infinite temperature. However, for 0 < D < 1, the SRPS are nonergodic and fractal, as they are confined in a vanishing ratio N D / N of the full Hilbert space. Both analytically and numerically, we show that the mean entanglement entropy S1(A) of a subsystem A, with Hilbert space dimension NA, scales as 1(A) ∼ D ln N for small fractal dimensions D, N D < NA. Remarkably, 1(A) saturates at its thermal (Page) value at an infinite temperature, 1(A) ∼ ln NA at larger D. Consequently, we provide an example when the entanglement entropy takes an ergodic value even though the wave function is highly nonergodic. Finally, we generalize our results to Renyi entropies Sq (A) with q > 1 and to genuine multifractal states and also show that their fluctuations have ergodic behavior in a narrower vicinity of the ergodic state D = 1.

Phys. Rev. Lett. 124, 200602 (2020)





Pyrochlore S=1/2 Heisenberg antiferromagnet at finite temperature
R. Schäfer, I. Hagymási, R. Moessner, and D. J. Luitz

We use a combination of three computational methods to investigate the notoriously difficult frustrated three-dimensional pyrochlore S=1/2 quantum antiferromagnet, at finite temperature T: canonical typicality for a finite cluster of 2×2×2 unit cells (i.e., 32 sites), a finite-T matrix product state method on a larger cluster with 48 sites, and the numerical linked cluster expansion (NLCE) using clusters up to 25 lattice sites, including nontrivial hexagonal and octagonal loops. We calculate thermodynamic properties (energy, specific heat capacity, entropy, susceptibility, magnetization) and the static structure factor. We find a pronounced maximum in the specific heat at T=0.57J, which is stable across finite size clusters and converged in the series expansion. At T≈0.25J (the limit of convergence of our method), the residual entropy per spin is 0.47kB ln 2, which is relatively large compared to other frustrated models at this temperature. We also observe a nonmonotonic dependence on T of the magnetization at low magnetic fields, reflecting the dominantly nonmagnetic character of the low-energy states. A detailed comparison of our results to measurements for the S=1 material NaCaNi2F7 yields a rough agreement of the functional form of the specific heat maximum, which in turn differs from the sharper maximum of the heat capacity of the spin ice material Dy2Ti2O7.

Phys. Rev. B 102, 054408 (2020)




Prethermalization without Temperature
D. J. Luitz, R. Moessner, S. L. Sondhi, V. Khemani

While a clean, driven system generically absorbs energy until it reaches “infinite temperature,” it may do so very slowly exhibiting what is known as a prethermal regime. Here, we show that the emergence of an additional approximately conserved quantity in a periodically driven (Floquet) system can give rise to an analogous long-lived regime. This can allow for nontrivial dynamics, even from initial states that are at a high or infinite temperature with respect to an effective Hamiltonian governing the prethermal dynamics. We present concrete settings with such a prethermal regime, one with a period-doubled (time-crystalline) response. We also present a direct diagnostic to distinguish this prethermal phenomenon from its infinitely long-lived many- body localized cousin. We apply these insights to a model of the recent NMR experiments by Rovny et al. [Phys. Rev. Lett. 120, 180603 (2018)] which, intriguingly, detected signatures of a Floquet time crystal in a clean three-dimensional material. We show that a mild but subtle variation of their driving protocol can increase the lifetime of the time-crystalline signal by orders of magnitude.

Phys. Rev. X 10, 021046 (2020)





Anyons and fractional quantum Hall effect in fractal dimensions
S. Manna, B. Pal, W. Wang, and A. E. B. Nielsen

The fractional quantum Hall effect is a paradigm of topological order and has been studied thoroughly in two dimensions. Here, we construct a different type of fractional quantum Hall system, which has the special property that it lives in fractal dimensions. We provide analytical wave functions and exact few-body parent Hamiltonians, and we show numerically for several different Hausdorff dimensions between 1 and 2 that the systems host anyons. We also find examples of fractional quantum Hall physics in fractals with Hausdorff dimension 1 and ln(4)/ln(5). Our results suggest that the local structure of the investigated fractals is more important than the Hausdorff dimension to determine whether the systems are in the desired topological phase. The study paves the way for further investigations of strongly correlated topological systems in fractal dimensions.

Phys. Rev. Research 2, 023401 (2020)




Hierarchy of Relaxation Timescales in Local Random Liouvillians
Kevin Wang, Francesco Piazza, and David J. Luitz

To characterize the generic behavior of open quantum systems, we consider random, purely dissipative Liouvillians with a notion of locality. We find that the positivity of the map implies a sharp separation of the relaxation timescales according to the locality of observables. Specifically, we analyze a spin-1/2 system of size l with up to n-body Lindblad operators, which are n local in the complexity-theory sense. Without locality (n=l), the complex Liouvillian spectrum densely covers a “lemon”-shaped support, in agreement with recent findings [S. Denisov et al., Phys. Rev. Lett. 123, 140403 (2019)]. However, for local Liouvillians (n<l), we find that the spectrum is composed of several dense clusters with random matrix spacing statistics, each featuring a lemon-shaped support wherein all eigenvectors correspond to n-body decay modes. This implies a hierarchy of relaxation timescales of n-body observables, which we verify to be robust in the thermodynamic limit. Our findings for n locality generalize immediately to the case of spatial locality, introducing further splitting of timescales due to the additional structure.

Phys. Rev. Lett. 124, 100604 (2020)