Dynamical Signatures of Chaos to Integrability Crossover in $2\times 2$ Generalized Random Matrix Ensembles

• URL: http://arxiv.org/abs/2010.16394v2
• Date: Mon, 13 Nov 2023 23:59:15 GMT
• Title: Dynamical Signatures of Chaos to Integrability Crossover in $2\times 2$ Generalized Random Matrix Ensembles
• Authors: Adway Kumar Das, Anandamohan Ghosh
• Abstract summary: We study the energy correlations by calculating the density and 2nd moment of the Nearest Neighbor Spacing (NNS) We observe that for large $N$ the 2nd moment of NNS and the relative depth of the correlation hole exhibit a second order phase transition at $gamma=2$.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a two-parameter ensemble of generalized $2\times 2$ real symmetric random matrices called the $\beta$-Rosenzweig-Porter ensemble (\brpe), parameterized by $\beta$, a fictitious inverse temperature of the analogous Coulomb gas model, and $\gamma$, controlling the relative strength of disorder. \brpe\ encompasses RPE from all of the Dyson's threefold symmetry classes: orthogonal, unitary and symplectic for $\beta=1,2,4$. Firstly, we study the energy correlations by calculating the density and 2nd moment of the Nearest Neighbor Spacing (NNS) and robustly quantify the crossover among various degrees of level repulsions. Secondly, the dynamical properties are determined from an exact calculation of the temporal evolution of the fidelity enabling an identification of the characteristic Thouless and the equilibration timescales. The relative depth of the correlation hole in the average fidelity serves as a dynamical signature of the crossover from chaos to integrability and enables us to construct the phase diagram of \brpe\ in the $\gamma$-$\beta$ plane. Our results are in qualitative agreement with numerically computed fidelity for $N\gg2$ matrix ensembles. Furthermore, we observe that for large $N$ the 2nd moment of NNS and the relative depth of the correlation hole exhibit a second order phase transition at $\gamma=2$.

Related papers

• Two-dopant origin of competing stripe and pair formation in Hubbard and $t$-$J$ models [0.0]
  We study single pairs of dopants in a cylindrical system using the density-matrix renormalization group algorithm. We establish that the interplay between order and uniform pairing, central to the models' phases at finite doping, has its origin at the single-pair level.
  arXiv  Detail & Related papers  (2024-09-26T17:59:57Z)
• KPZ scaling from the Krylov space [83.88591755871734]
  Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang scaling in late-time correlators and autocorrelators has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis.
  arXiv  Detail & Related papers  (2024-06-04T20:57:59Z)
• Ancilla quantum measurements on interacting chains: Sensitivity of entanglement dynamics to the type and concentration of detectors [46.76612530830571]
  We consider a quantum many-body lattice system that is coupled to ancillary degrees of freedom (detectors'') We explore the dynamics of density and of entanglement entropy in the chain, for various values of $rho_a$ and $M$.
  arXiv  Detail & Related papers  (2023-11-21T21:41:11Z)
• Spectral crossover in non-hermitian spin chains: comparison with random matrix theory [1.0793830805346494]
  We study the short range spectral fluctuation properties of three non-hermitian spin chain hamiltonians using complex spacing ratios. The presence of a random field along the $x$-direction together with the one along $z$ facilitates integrability and $mathcalRT$-symmetry breaking.
  arXiv  Detail & Related papers  (2023-02-02T21:26:44Z)
• Superdiffusion in random two dimensional system with time-reversal symmetry and long-range hopping [45.873301228345696]
  localization problem in the crossover regime for the dimension $d=2$ and hopping $V(r) propto r-2$ is not resolved yet. We show that for the hopping determined by two-dimensional anisotropic dipole-dipole interactions there exist two distinguishable phases at weak and strong disorder.
  arXiv  Detail & Related papers  (2022-05-29T16:53:20Z)
• Universal Entanglement Transitions of Free Fermions with Long-range Non-unitary Dynamics [16.533265279392772]
  Non-unitary evolution can give rise to novel steady states classified by their entanglement properties. In this work, we aim to understand its interplay with long-range hopping that decays with $r-alpha$ in free-fermion systems.
  arXiv  Detail & Related papers  (2021-05-19T02:52:48Z)
• Symmetry from Entanglement Suppression [0.0]
  We show that a minimally entangling $S$-matrix would give rise to global symmetries. For $N_q$ species of qubit, the Identity gate is associated with an $[SU(2)]N_q$ symmetry.
  arXiv  Detail & Related papers  (2021-04-22T02:50:10Z)
• Entanglement and U(D)-spin squeezing in symmetric multi-quDit systems and applications to quantum phase transitions in Lipkin-Meshkov-Glick D-level atom models [0.0]
  Collective spin operators for symmetric multi-quDit systems generate a U$(D)$ symmetry. We explore generalizations to arbitrary $D$ of SU(2)-spin coherent states and their adaptation to parity. We evaluate level and particle entanglement for symmetric multi-quDit states with linear and von Neumann entropies.
  arXiv  Detail & Related papers  (2021-04-21T15:19:43Z)
• Boundary time crystals in collective $d$-level systems [64.76138964691705]
  Boundary time crystals are non-equilibrium phases of matter occurring in quantum systems in contact to an environment. We study BTC's in collective $d$-level systems, focusing in the cases with $d=2$, $3$ and $4$.
  arXiv  Detail & Related papers  (2021-02-05T19:00:45Z)
• Optimal Robust Linear Regression in Nearly Linear Time [97.11565882347772]
  We study the problem of high-dimensional robust linear regression where a learner is given access to $n$ samples from the generative model $Y = langle X,w* rangle + epsilon$ We propose estimators for this problem under two settings: (i) $X$ is L4-L2 hypercontractive, $mathbbE [XXtop]$ has bounded condition number and $epsilon$ has bounded variance and (ii) $X$ is sub-Gaussian with identity second moment and $epsilon$ is
  arXiv  Detail & Related papers  (2020-07-16T06:44:44Z)
• Anisotropy-mediated reentrant localization [62.997667081978825]
  We consider a 2d dipolar system, $d=2$, with the generalized dipole-dipole interaction $sim r-a$, and the power $a$ controlled experimentally in trapped-ion or Rydberg-atom systems. We show that the spatially homogeneous tilt $beta$ of the dipoles giving rise to the anisotropic dipole exchange leads to the non-trivial reentrant localization beyond the locator expansion.
  arXiv  Detail & Related papers  (2020-01-31T19:00:01Z)

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.