We present a large scale exact diagonalization study 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, volumelaw 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. The interplay of disorder and interactions in quantum systems can lead to several intriguing phenomena, amongst which the so-called many-body localization has attracted a huge interest in recent years. Following precursors works [1][2][3][4], perturbative calculations [5,6] have established that the celebrated Anderson localization [7] can survive interactions, and that for large enough disorder, many-body eigenstates can also "localize" (in a sense to be precised later) and form a new phase of matter commonly referred to as the many-body localized (MBL) phase.The enormous boost of interest for this topic over the last years can probably be ascribed to the fact that the MBL phase challenges the very foundations of quantum statistical physics, leading to striking theoretical and experimental consequences [8,9]. Several key features of the MBL phase can be highlighted as follows. It is nonergodic, and breaks the eigenstate thermalization hypothesis (ETH) [10][11][12]: a closed system in the MBL phase does not thermalize solely following its own dynamics. The possible presence of a many-body mobility edge (at a finite energy density in the spectrum) indicates that conductivity should vanish in a finite temperature range in a MBL system [5,6]. Coupling to an external bath will eventually destroy the properties of the MBL phase, but recent arguments show that it can survive and be detected using spectral signatures for weak bath-coupling [13]. This leads to the suggestion that the MBL phase can be characterized experimentally, using e.g. controlled echo experiments on reasonably well-isolated systems with dipolar interactions [14][15][16][17]. Another appealing aspect (with experimental consequences for self-correcting memories) is that MBL systems can sustain long-range, possibly topological, order in situations where equilibrated systems would not [18][19][20][21][22]. Finally, a striking phenomenological approach [23] pinpoints that the MBL phase shares properties with integrable systems, with extensive local integrals of mo- ∈ {14, 15, 16, 17, 18, 19, 20, 22}. Red squares correspond to a visual e...

5 pages, 3 figuresInternational audienceMany-body localization is characterized by a slow logarithmic growth of the entanglement entropy after a global quantum quench while the local memory of an initial density imbalance remains at infinite time. We investigate how much the proximity of a many-body localized phase can influence the dynamics in the delocalized ergodic regime where thermalization is expected. Using an exact Krylov space technique, the out-of-equilibrium dynamics of the random-field Heisenberg chain is studied up to L=28 sites, starting from an initially unentangled high-energy product state. Within most of the delocalized phase, we find a sub-ballistic entanglement growth $S(t)\propto t^{1/z}$ with a disorder-dependent exponent $z\ge1$, in contrast with the pure ballistic growth $z=1$ of clean systems. At the same time, anomalous relaxation is also observed for the spin imbalance $I(t) \propto t^{-\zeta}$ with a continuously varying disorder-dependent exponent $\zeta$, vanishing at the transition. This provides a clear experimental signature for detecting this non-conventional regime

We present release 1.3 of the ALPS (Algorithms and Libraries for Physics Simulations) project, an international open source software project to develop libraries and application programs for the simulation of strongly correlated quantum lattice models such as quantum magnets, lattice bosons, and strongly correlated fermion systems. Development is centered on common XML and binary data formats, on libraries to simplify and speed up code development, and on full-featured simulation programs. The programs enable non-experts to start carrying out numerical simulations by providing basic implementations of the important algorithms for quantum lattice models: classical and quantum Monte Carlo (QMC) using non-local updates, extended ensemble simulations, exact and full diagonalization (ED), as well as the density matrix renormalization group (DMRG). Changes in the new release include a DMRG program for interacting models, support for translation symmetries in the diagonalization programs, the ability to define custom measurement operators, and support for inhomogeneous systems, such as lattice models with traps. The software is available from our web server at http://alps.comp-phys.org/.

No abstract

We study the nature of the ground state of the two-dimensional extended boson Hubbard model on a square lattice by quantum Monte Carlo methods. We demonstrate that strong but finite on-site interaction U along with a comparable nearest-neighbor repulsion V result in a thermodynamically stable supersolid ground state for densities larger than 1/2, in contrast to fillings less than 1/2 or for very large U, where the checkerboard supersolid is unstable towards phase separation. We discuss the relevance of our results to realizations of supersolids using cold bosonic atoms in optical lattices.

The behavior of the ground-state fidelity susceptibility in the vicinity of a quantum critical point is investigated. We derive scaling relations describing its singular behavior in the quantum critical regime. Unlike in previous studies, these relations are solely expressed in terms of conventional critical exponents. We also describe in detail a quantum Monte Carlo scheme that allows for the evaluation of the fidelity susceptibility for a large class of many-body systems and apply it in the study of the quantum phase transition for the transverse-field Ising model on the square lattice. Finite size analysis applied to the so obtained numerical results confirm the validity of our scaling relations. Furthermore, we analyze the properties of a closely related quantity, the ground-state energy's second derivative, that can be numerically evaluated in a particularly efficient way. The usefulness of both quantities as alternative indicators of quantum criticality is examined.

In the presence of sufficiently strong disorder or quasiperiodic fields, an interacting many-body system can fail to thermalize and become many-body localized. The associated transition is of particular interest, since it occurs not only in the ground state but over an extended range of energy densities. So far, theoretical studies of the transition have focused mainly on the case of true-random disorder. In this work, we experimentally and numerically investigate the regime close to the many-body localization transition in quasiperiodic systems. We find slow relaxation of the density imbalance close to the transition, strikingly similar to the behavior near the transition in true-random systems. This dynamics is found to continuously slow down upon approaching the transition and allows for an estimate of the transition point. We discuss possible microscopic origins of these slow dynamics.

The Néel temperature, TN, of quasi-one-and quasi-two-dimensional antiferromagnetic Heisenberg models on a cubic lattice is calculated by Monte Carlo simulations as a function of inter-chain (interlayer) to intra-chain (intra-layer) coupling J ′ /J down to J ′ /J ≃ 10 −3 . We find that TN obeys a modified random-phase approximation-like relation for small J ′ /J with an effective universal renormalized coordination number, independent of the size of the spin. Empirical formulae describing TN for a wide range of J ′ and useful for the analysis of experimental measurements are presented.While genuinely one-dimensional (1D) and two-dimensional (2D) antiferromagnetic Heisenberg (AFH) models cannot display long-range order (LRO) except at zero temperature [1], weak inter-chain or inter-layer couplings, J ′ , which always exist in real materials, lead to a finite Néel temperature T N . So far, the J ′ -dependence of T N was calculated by exactly treating effects of the strong interaction J in the 1D or 2D system, but using mean-field approximations for the inter-chain and interlayer coupling. Recently, more advanced theories of the latter effects have been proposed for quasi-1D (Q1D) [3,4] and quasi-2D (Q2D) [5] systems, and the results have been compared with the experimental observations on Q1D antiferromagnets, e.g., Sr 2 CuO 3 [6], and Q2D antiferromagnets, e.g., La 2 CuO 4 [7]. In view of the importance of experimentally well-studied Q2D antiferromagnets as undoped parent compounds of the high-temperature superconductors, accurate and unbiased numerical results for Q1D and Q2D AFH models are strongly desired. In a recent work along this line, Sengupta et al. [8] have demonstrated peculiar temperature dependences of the specific heat in the quantum Q2D AFH model.Here we calculate the Néel temperature T N as a function of J ′ in fully three-dimensional (3D) classical and quantum Monte Carlo (MC) simulations of coupledchains and coupled-layers. Our MC results on the quantum spin-S and classical S = ∞ AFH models are analyzed by a modified random-phase approximation (RPA) with a renormalized coordination number defined bywhere χ s (T ) is the staggered susceptibility of the 1D or 2D model at temperature T . In a simple RPA calculation [2], this quantity is just the coordination number z d in the inter-chain or inter-layer directions: z 1 = 4 and z 2 = 2 for the Q1D and Q2D systems, respectively. Our main result is that ζ(J ′ ) evaluated by Eq. (1) with our numerically obtained T N (J ′ ) and χ s (T ) becomes constant, with the constants k 1 = 0.695 and k 2 = 0.65. These constants k d differ from the simple RPA result k d = 1, but the value of k 1 is consistent with the modified self-consistent RPA theory for the quantum Q1D (q-Q1D) model of Irkhin and Katanin (IK) [3]. Furthermore we find, that, within our numerical accuracy, the value of k d is the same for the S = 1/2, S = 1, S = 3/2 and S = ∞, and we conjecture that k d is universal and independent of the spin S for small J ′ /J. We also propose empirical formulae ...