We analyze the role of the interplay between on-site interaction and inhomogeneous diffusion on the phenomenon of condensation in the zero-range process. We predict a universal phase diagram in the plane of two exponents, respectively characterizing the interactions and the diffusion disorder. The most prominent outcome is the existence of an extended condensed phase. In the latter phase, which originates as a result of the combined effects of strong enough interaction and weak enough disorder, a typical high-density configuration has a unique condensate on top of a critical background, but the condensate may be located at any site of a large hosting set of favored sites, whose size grows sub-extensively. The novel extended condensed phase thus interpolates continuously between the two scenarios associated so far with the condensation transition, namely spontaneous symmetry breaking and explicit symmetry breaking.
The zero range process is of particular importance as a generic model for domain wall dynamics of one-dimensional systems far from equilibrium. We study this process in one dimension with rates which induce an effective attraction between particles. We rigorously prove that for the stationary probability measure there is a background phase at some critical density and for large system size essentially all excess particles accumulate at a single, randomly located site. Using random walk arguments supported by Monte Carlo simulations, we also study the dynamics of the clustering process with particular attention to the difference between symmetric and asymmetric jump rates. For the late stage of the clustering we derive an effective master equation, governing the occupation number at clustering sites. Key words: zero range process; nonequilibrium phase transition; equivalence of ensembles; relative entropy. 1
We consider the phenomenon of condensation of a globally conserved quantity $H={\ensuremath{\sum}}_{i=1}^{N}{\ensuremath{\epsilon}}_{i}$ distributed on
N sites, occurring when the density
h=H/N exceeds a critical density
hc. We numerically study the dependence of the participation ratio ${Y}_{2}=\ensuremath{\langle}{\ensuremath{\epsilon}}_{i}^{2}\ensuremath{\rangle}/(N{h}^{2})$ on the size
N of the system and on the control parameter $\ensuremath{\delta}=(h\ensuremath{-}{h}_{c})$, for various models: (i) a model with two conservation laws, derived from the discrete nonlinear Schr\"odinger equation; (ii) the continuous version of the zero-range process class, for different forms of the function $f(\ensuremath{\epsilon})$ defining the factorized steady state. Our results show that various localization scenarios may appear for finite
N and close to the transition point. These scenarios are characterized by the presence or the absence of a minimum of
Y2 when plotted against
N and by an exponent $\ensuremath{\gamma}\ensuremath{\ge}2$ defined through the relation ${N}^{*}\ensuremath{\simeq}{\ensuremath{\delta}}^{\ensuremath{-}\ensuremath{\gamma}}$, where
N∗ separates the delocalized region ($N\ensuremath{\ll}{N}^{*}$,
Y2 vanishes with increasing
N) from the localized region ($N\ensuremath{\gg}{N}^{*}$,
Y2 is approximately constant). We finally compare our results with the structure of the condensate obtained through the single-site marginal distribution.
Bose-Einstein-condensed gases in external spatially random potentials are considered in the frame of a stochastic self-consistent mean-field approach. This method permits the treatment of the system properties for the whole range of the interaction strength, from zero to infinity, as well as for arbitrarily strong disorder. Besides a condensate and superfluid density, a glassy number density due to a spatially inhomogeneous component of the condensate occurs. For very weak interactions and sufficiently strong disorder, the superfluid fraction can become smaller than the condensate fraction, while at relatively strong interactions, the superfluid fraction is larger than the condensate fraction for any strength of disorder. The condensate and superfluid fractions, and the glassy fraction always coexist, being together either nonzero or zero. In the presence of disorder, the condensate fraction becomes a nonmonotonic function of the interaction strength, displaying an antidepletion effect caused by the competition between the stabilizing role of the atomic interaction and the destabilizing role of the disorder. With increasing disorder, the condensate and superfluid fractions jump to zero at a critical value of the disorder parameter by a first-order phase transition.
The interplay between topology and correlation lies at the forefront of modern condensed matter physics. In this paper, we study the extended fermion-Hubbard model, including the on-site as well as the nearest-neighbor repulsive interactions, on a topological square lattice that supports the Chern insulator. Within the mean-field method, we find that the spontaneous symmetry breaking (SSB) charge-density wave or antiferromagnetic insulator dominates the system when the onsite or nearest-neighbor interactions are strong enough. It is interesting that the antiferromagnetic Chern insulator will appear in the phase diagram when there is an explicitly nonvanishing sublattice potential. In addition, we explore how a finite-size ribbon structure affects the phase diagram and point out that the critical interaction for SSB occurs with weaker strength than the bulk system.
Using the density matrix renormalization group algorithm, we map the ground-state phase diagram of a two-leg Rydberg ladder array with lattice spacings
ax=2ay. We identify various density wave phases that spontaneously break the translational symmetry or the top-bottom reflection symmetry within the ladder. By increasing the laser detuning from zero, where the system is in a disordered phase that preserves all symmetries, we observe density wave orders with spontaneous breaking of the translational
Zp symmetries at intermediate detuning values, while the reflection symmetry is preserved. These orders exhibit nonzero bond orders with positive expectation values on every
pth rung, thus labeled as
Zp+ phases. At larger detuning values, another spontaneous breaking of the reflection symmetry, which disrupted the bond orders on the rungs, occurs via an Ising phase transition. In these phases, either the top or the bottom site is occupied in a staggered way on every
pth rung, breaking the translational
Z2p symmetry, thus labeled by
Z2p phases. We locate and characterize the 3-state Potts point and Ashkin-Teller point along the commensurate lines, as well as the direct chiral phase transitions between the disordered phase and the
Zp+ (p=3,4) phases. Critical exponents $\ensuremath{\nu}$ and
z are calculated for both conformal and chiral phase transition points. We finally identify two types of floating phases in the phase diagram: one characterized by a quasi-long-range incommensurate bond-order wave, and the other by a quasi-long-range incommensurate wave of density differences in the rungs. Our work motivates further applications of Rydberg atom arrays in quantum simulation.
The zero-range process, in which particles hop between sites on a lattice under conserving dynamics, is a prototypical model for studying real-space condensation. Within this model the system is critical only at the transition point. Here we consider a non-conserving zero-range process which is shown to exhibit generic critical phases which exist in a range of creation and annihilation parameters. The model also exhibits phases characterized by mesocondensates, each of which contains a subextensive number of particles. A detailed phase diagram, delineating the various phases, is derived.