David A. Huse

Many-Body Localization and Thermalization in Quantum Statistical Mechanics

We review some recent developments in the statistical mechanics of isolated quantum systems. We provide a brief introduction to quantum thermalization, paying particular attention to the eigenstate thermalization hypothesis (ETH) and the resulting single-eigenstate statistical mechanics. We then focus on a class of systems that fail to quantum thermalize and whose eigenstates violate the ETH: These are the many-body Anderson-localized systems; their long-time properties are not captured by the conventional ensembles of quantum statistical mechanics. These systems can forever locally remember information about their local initial conditions and are thus of interest for possibilities of storing quantum information. We discuss key features of many-body localization (MBL) and review a phenomenology of the MBL phase. Single-eigenstate statistical mechanics within the MBL phase reveal dynamically stable ordered phases, and phase transitions among them, that are invisible to equilibrium statistical mechanics and...

Spin-Liquid Ground State of the S = 1/2 Kagome Heisenberg Antiferromagnet

Numerical calculations reveal that the true ground state of a frustrated two-dimensional system is a gapped spin liquid. We use the density matrix renormalization group to perform accurate calculations of the ground state of the nearest-neighbor quantum spin S = 1/2 Heisenberg antiferromagnet on the kagome lattice. We study this model on numerous long cylinders with circumferences up to 12 lattice spacings. Through a combination of very-low-energy and small finite-size effects, our results provide strong evidence that, for the infinite two-dimensional system, the ground state of this model is a fully gapped spin liquid.

Entropy difference between crystal phases

In a recent Letter, Woodcock reported the results of a molecular dynamics study in which he claims to have finally determined the free-energy difference between the hexagonal close-packed (h.c.p.) and face-centred cubic (f.c.c.) phases of a crystal of (classical) hard spheres. Woodcock reports a small positive difference in the reduced Gibbs free-energy, which is equivalent to a difference in the reduced Helmholtz free-energy of ΔF*≡(Fhcp −Ffcc)/RT=0.005(1) at the melting density (R is the gas constant, T is the absolute temperature, and the number in parentheses is the estimated error in the last digit). As Woodcock correctly points out, the calculation of the relative stability of the f.c.c. and h.c.p. phases of hard spheres is a long-standing problem in statistical physics. Attempts to resolve it date back to the work of Alder, Hoover and colleagues, and most recently, a direct simulation by Frenkel and Ladd, obtaining the bounds of Helmholtz free-energy of −0.001⩽ΔF*⩽0.002. Woodcocks estimate is incompatible with this latter result.

Phenomenology of fully many-body-localized systems

Initiative for the Theoretical Sciences, The Graduate Center, CUNY, New York, NY 10016, USA(Dated: August 20, 2014)We consider fully many-body localized systems, i.e. isolated quantum systems where all themany-body eigenstates of the Hamiltonian are localized. We define a sense in which such systems areintegrable, with localized conserved operators. These localized operators are interacting pseudospins,and the Hamiltonian is such that unitary time evolution produces dephasing but not ‘flips’ of thesepseudospins. As a result, an initial quantum state of a pseudospin can in principle be recoveredvia (pseudospin) echo procedures. We discuss how the exponentially decaying interactions betweenpseudospins lead to logarithmic-in-time spreading of entanglement starting from nonentangled initialstates. These systems exhibit multiple different length scales that can be defined from exponentialfunctions of distance; we suggest that some of these decay lengths diverge at the phase transitionout of the fully many-body localized phase while others remain finite.

Exploring the many-body localization transition in two dimensions

Bosons refusing to thermalize in 2D Messy, interacting quantum-mechanical systems are difficult to analyze theoretically. In a single spatial dimension, the calculations are still tractable, and experiments have recently confirmed the prediction that sufficiently strong disorder can disrupt the transport of interacting particles. In two dimensions, however, the theoretical blueprint is missing. Choi et al. used single-site imaging of cold 87Rb atoms in an optical lattice to show that similar localization occurs in two-dimensional (2D) systems. The study highlights the power of quantum simulation to solve problems that are currently inaccessible to classical computing techniques. Science, this issue p. 1547 Single-site imaging in a two-dimensional optical lattice filled with interacting rubidium atoms shows that disorder can prevent thermalization. A fundamental assumption in statistical physics is that generic closed quantum many-body systems thermalize under their own dynamics. Recently, the emergence of many-body localized systems has questioned this concept and challenged our understanding of the connection between statistical physics and quantum mechanics. Here we report on the observation of a many-body localization transition between thermal and localized phases for bosons in a two-dimensional disordered optical lattice. With our single-site–resolved measurements, we track the relaxation dynamics of an initially prepared out-of-equilibrium density pattern and find strong evidence for a diverging length scale when approaching the localization transition. Our experiments represent a demonstration and in-depth characterization of many-body localization in a regime not accessible with state-of-the-art simulations on classical computers.

Many-body localization in a quantum simulator with programmable random disorder

Interacting quantum systems are expected to thermalize, but in some situations in the presence of disorder they can exist in localized states instead. This many-body localization is studied experimentally in a small system with programmable disorder. When a system thermalizes it loses all memory of its initial conditions. Even within a closed quantum system, subsystems usually thermalize using the rest of the system as a heat bath. Exceptions to quantum thermalization have been observed, but typically require inherent symmetries1,2 or noninteracting particles in the presence of static disorder3,4,5,6. However, for strong interactions and high excitation energy there are cases, known as many-body localization (MBL), where disordered quantum systems can fail to thermalize7,8,9,10. We experimentally generate MBL states by applying an Ising Hamiltonian with long-range interactions and programmable random disorder to ten spins initialized far from equilibrium. Using experimental and numerical methods we observe the essential signatures of MBL: initial-state memory retention, Poissonian distributed energy level spacings, and evidence of long-time entanglement growth. Our platform can be scaled to more spins, where a detailed modelling of MBL becomes impossible.

Stacking entropy of hard-sphere crystals

Classical hard spheres crystallize at equilibrium at high enough density. Crystals made up of stackings of two-dimensional hexagonal close-packed layers (e.g., fcc, hcp, etc.) differ in entropy by only about

Magnetic Flux-Line Lattices and Vortices in the Copper Oxide Superconductors

{10}^{\ensuremath{-}3}{k}_{B}

Optimizing the ensemble for equilibration in broad-histogram Monte Carlo simulations.

per sphere (all configurations are degenerate in energy). To readily resolve and study these small entropy differences, we have implemented two different multicanonical Monte Carlo algorithms that allow direct equilibration between crystals with different stacking sequences. Recent work had demonstrated that the fcc stacking has higher entropy than the hcp stacking. We have studied other stackings to demonstrate that the fcc stacking does indeed have the highest entropy of all possible stackings. The entropic interactions we could detect involve three, four, and (although with less statistical certainty) five consecutive layers of spheres. These interlayer entropic interactions fall off in strength with increasing distance, as expected; this falloff appears to be much slower near the melting density than at the maximum (close-packing) density. At maximum density the entropy difference between fcc and hcp stackings is

Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms

0.00115\ifmmode\pm\else\textpm\fi{}0.00004{k}_{B}