Detecting delocalization-localization transitions from full density
distributions
- URL: http://arxiv.org/abs/2105.10584v2
- Date: Mon, 29 Nov 2021 23:11:24 GMT
- Title: Detecting delocalization-localization transitions from full density
distributions
- Authors: Miroslav Hopjan, Giuliano Orso, Fabian Heidrich-Meisner
- Abstract summary: Characterizing the delocalization transition in closed quantum systems with a many-body localized phase is a key open question in the field of nonequilibrium physics.
We study its scaling behavior across delocalozation transitions and identify critical points from scaling collapses of numerical data.
We observe a distinctively different scaling behavior in the case of interacting fermions with random disorder consistent with a Kosterlitz-Thouless transition.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Characterizing the delocalization transition in closed quantum systems with a
many-body localized phase is a key open question in the field of nonequilibrium
physics. We exploit that localization of particles as realized in Anderson and
standard many-body localization (MBL) implies Fock-space localization in
single-particle basis sets characterized by a real-space index. Using a
recently introduced quantitative measure for Fock-space localization computed
from the density distributions, the occupation distance, we systematically
study its scaling behavior across delocalozation transitions and identify
critical points from scaling collapses of numerical data. Excellent agreement
with literature results is found for the critical disorder strengths of
noninteracting fermions, such as the one-dimensional Aubry-Andr\'e and the
three-dimensional Anderson model. We observe a distinctively different scaling
behavior in the case of interacting fermions with random disorder consistent
with a Kosterlitz-Thouless transition. Finally, we use our measure to extract
the transition point as a function of filling for interacting fermions.
Related papers
- Information Bounds on phase transitions in disordered systems [0.0]
We study phase transitions in models with randomness, such as localization in disordered systems, or random quantum circuits with measurements.
We benchmark our method and rederive the well-known Harris criterion, bounding critical exponents in the Anderson localization transition for noninteracting particles.
While in real space our critical exponent bound agrees with recent consensus, we find that, somewhat surprisingly, numerical results on Fock-space localization for limited-sized systems do not obey our bounds.
arXiv Detail & Related papers (2023-08-29T18:00:07Z) - Many-body Localization in Clean Chains with Long-Range Interactions [2.538209532048867]
Author numerically investigates thermalization and many-body localization in translational invariant quantum chains.
The long-time dynamics is dominated by the homogeneity eigenstates and eventually reach degenerate in real space.
On the other hand, the entanglement entropy exhibits the size-dependence beyond the area law for the same reason, even deep in the localized state.
arXiv Detail & Related papers (2023-06-19T04:06:06Z) - Entanglement and localization in long-range quadratic Lindbladians [49.1574468325115]
Signatures of localization have been observed in condensed matter and cold atomic systems.
We propose a model of one-dimensional chain of non-interacting, spinless fermions coupled to a local ensemble of baths.
We show that the steady state of the system undergoes a localization entanglement phase transition by tuning $p$ which remains stable in the presence of coherent hopping.
arXiv Detail & Related papers (2023-03-13T12:45:25Z) - Full counting statistics as probe of measurement-induced transitions in
the quantum Ising chain [62.997667081978825]
We show that local projective measurements induce a modification of the out-of-equilibrium probability distribution function of the local magnetization.
In particular we describe how the probability distribution of the former shows different behaviour in the area-law and volume-law regimes.
arXiv Detail & Related papers (2022-12-19T12:34:37Z) - Measurements on an Anderson Chain [0.0]
We study the dynamics of a monitored single particle in a one-dimensional, Anderson-localized system.
We find that measurements at random positions delocalize the average position, similar to a classical random walk.
In contrast to measurement-induced delocalization, controlled measurements can be used to introduce transport in the system and localize the particle at a chosen site.
arXiv Detail & Related papers (2022-11-11T16:49:05Z) - Localization in the random XXZ quantum spin chain [55.2480439325792]
We study the many-body localization (MBL) properties of the Heisenberg XXZ spin-$frac12$ chain in a random magnetic field.
We prove that the system exhibits localization in any given energy interval at the bottom of the spectrum in a nontrivial region of the parameter space.
arXiv Detail & Related papers (2022-10-26T17:25:13Z) - Localization properties of the asymptotic density distribution of a
one-dimensional disordered system [0.0]
Anderson localization is the ubiquitous phenomenon of inhibition of transport of classical and quantum waves in a disordered medium.
The exact shape of the stationary localized distribution differs from a purely exponential profile and has been computed almost fifty years ago by Gogolin.
Using the atomic quantum kicked rotor, a paradigmatic quantum simulator of Anderson localization physics, we study this distribution.
arXiv Detail & Related papers (2022-03-16T09:40:39Z) - Locality of Spontaneous Symmetry Breaking and Universal Spacing
Distribution of Topological Defects Formed Across a Phase Transition [62.997667081978825]
A continuous phase transition results in the formation of topological defects with a density predicted by the Kibble-Zurek mechanism (KZM)
We characterize the spatial distribution of point-like topological defects in the resulting nonequilibrium state and model it using a Poisson point process in arbitrary spatial dimension with KZM density.
arXiv Detail & Related papers (2022-02-23T19:00:06Z) - Determination of the critical exponents in dissipative phase
transitions: Coherent anomaly approach [51.819912248960804]
We propose a generalization of the coherent anomaly method to extract the critical exponents of a phase transition occurring in the steady-state of an open quantum many-body system.
arXiv Detail & Related papers (2021-03-12T13:16:18Z) - Rare thermal bubbles at the many-body localization transition from the
Fock space point of view [0.0]
We study the many-body localization (MBL) transition and relate it to the eigenstate structure in the Fock space.
We introduce the radial probability distribution of eigenstate coefficients with respect to the Hamming distance in the Fock space.
We show that the MBL transition can been seen as a transition between ergodic states to non-ergodic extended states.
arXiv Detail & Related papers (2020-11-05T19:00:01Z) - Observing localisation in a 2D quasicrystalline optical lattice [52.77024349608834]
We experimentally and numerically study the ground state of non- and weakly-interacting bosons in an eightfold symmetric optical lattice.
We find extended states for weak lattices but observe a localisation transition at a lattice depth of $V_0.78(2),E_mathrmrec$ for the non-interacting system.
arXiv Detail & Related papers (2020-01-29T15:54:42Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.