Spectral crossover in non-hermitian spin chains: comparison with random matrix theory

• URL: http://arxiv.org/abs/2302.01423v3
• Date: Fri, 13 Oct 2023 20:11:28 GMT
• Title: Spectral crossover in non-hermitian spin chains: comparison with random matrix theory
• Authors: Ayana Sarkar, Sunidhi Sen and Santosh Kumar
• Abstract summary: 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.
• Score: 1.0793830805346494
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We systematically study the short range spectral fluctuation properties of three non-hermitian spin chain hamiltonians using complex spacing ratios. In particular we focus on the non-hermitian version of the standard one-dimensional anisotropic XY model having intrinsic rotation-time-reversal ($\mathcal{RT}$) symmetry that has been explored analytically by Zhang and Song in [Phys.Rev.A {\bf 87}, 012114 (2013)]. The corresponding hermitian counterpart is also exactly solvable and has been widely employed as a toy model in several condensed matter physics problems. We show that the presence of a random field along the $x$-direction together with the one along $z$ facilitates integrability and $\mathcal{RT}$-symmetry breaking leading to the emergence of quantum chaotic behaviour indicated by a spectral crossover resembling Poissonian to Ginibre unitary ensemble (GinUE) statistics of random matrix theory. Additionally, we consider two $n \times n$ dimensional phenomenological random matrix models in which, depending upon crossover parameters, the fluctuation properties measured by the complex spacing ratios show an interpolation between 1D-Poisson to GinUE and 2D-Poisson to GinUE behaviour. Here 1D and 2D Poisson correspond to real and complex uncorrelated levels, respectively.

Related papers

• 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)
• Universality of spectral fluctuations in open quantum chaotic systems [1.1557918404865375]
  We study the non-Hermitian and non-unitary ensembles based on the symmetry of matrix elements. We show that the fluctuation statistics of these ensembles are universal and quantum chaotic systems belonging to OE, UE, and SE.
  arXiv  Detail & Related papers  (2024-01-08T18:30:18Z)
• Renormalization group and spectra of the generalized P\"oschl-Teller potential [0.0]
  We study the P"oschl-Teller potential $V(x) = alpha2 g_s sinh-2(alpha x) + alpha2 g_c cosh-2(alpha x)$, for every value of the dimensionless parameters $g_s$ and $g_c singularity. We show that supersymmetry of the potential, when present, is also spontaneously broken, along with conformal symmetry.
  arXiv  Detail & Related papers  (2023-08-08T21:44:55Z)
• Capturing dynamical correlations using implicit neural representations [85.66456606776552]
  We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
  arXiv  Detail & Related papers  (2023-04-08T07:55:36Z)
• Modeling the space-time correlation of pulsed twin beams [68.8204255655161]
  Entangled twin-beams generated by parametric down-conversion are among the favorite sources for imaging-oriented applications. We propose a semi-analytic model which aims to bridge the gap between time-consuming numerical simulations and the unrealistic plane-wave pump theory.
  arXiv  Detail & Related papers  (2023-01-18T11:29:49Z)
• Universal transition of spectral fluctuation in particle-hole symmetric system [0.0]
  We study the spectral properties of a system with particle-hole symmetry in random matrix setting. We observe a crossover from Poisson to Wigner-Dyson like behavior in average local ratio of spacing within a spectrum of single matrix.
  arXiv  Detail & Related papers  (2022-07-29T13:19:45Z)
• Mesoscopic M\"obius ladder lattices as non-Hermitian model systems [0.0]
  We focus on two realizations of non-Hermitian physics in mesoscopic systems. First, we consider spiral optical microcavities in which the asymmetric scattering between whispering gallery modes induces the non-Hermitian behaviour. Second, for parity-time (PT) symmetric ladder lattices we compare circular and M"obius geometries.
  arXiv  Detail & Related papers  (2022-05-03T17:10:36Z)
• Simultaneous Transport Evolution for Minimax Equilibria on Measures [48.82838283786807]
  Min-max optimization problems arise in several key machine learning setups, including adversarial learning and generative modeling. In this work we focus instead in finding mixed equilibria, and consider the associated lifted problem in the space of probability measures. By adding entropic regularization, our main result establishes global convergence towards the global equilibrium.
  arXiv  Detail & Related papers  (2022-02-14T02:23:16Z)
• Degeneracy and hidden symmetry -- an asymmetric quantum Rabi model with an integer bias [0.0]
  We investigate the hidden symmetry of the asymmetric quantum Rabi model (AQRM) with a half-integral bias (ibQRM$_ell$) The existence of such symmetry has been widely believed to cause the degeneration of the spectrum, that is, the crossings on the energy curves. In this paper we propose a conjectural relation between the symmetry and degeneracy for the ibQRM$_ell$ given explicitly.
  arXiv  Detail & Related papers  (2021-06-16T16:17:11Z)
• Rectification induced by geometry in two-dimensional quantum spin lattices [58.720142291102135]
  We address the role of geometrical asymmetry in the occurrence of spin rectification in two-dimensional quantum spin chains. We show that geometrical asymmetry, along with inhomogeneous magnetic fields, can induce spin current rectification even in the XX model.
  arXiv  Detail & Related papers  (2020-12-02T18:10:02Z)
• SU$(3)_1$ Chiral Spin Liquid on the Square Lattice: a View from Symmetric PEPS [55.41644538483948]
  Quantum spin liquids can be faithfully represented and efficiently characterized within the framework of Projectedangled Pair States (PEPS) Characteristic features are revealed by the entanglement spectrum (ES) on an infinitely long cylinder. Special features in the ES are shown to be in correspondence with bulk anyonic correlations, indicating a fine structure in the holographic bulk-edge correspondence.
  arXiv  Detail & Related papers  (2019-12-31T16:30:25Z)

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.