Spectral statistics in constrained many-body quantum chaotic systems

• URL: http://arxiv.org/abs/2009.11863v2
• Date: Mon, 4 Jan 2021 23:45:25 GMT
• Title: Spectral statistics in constrained many-body quantum chaotic systems
• Authors: Sanjay Moudgalya, Abhinav Prem, David A. Huse, Amos Chan
• Abstract summary: We study the spectral statistics of spatially-extended many-body quantum systems with on-site Abelian symmetries or local constraints. In particular, we analytically argue that in a system of length $L$ that conserves the $mth$ multipole moment, $t_mathrmTh$ scales subdiffusively as $L2(m+1)$.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the spectral statistics of spatially-extended many-body quantum systems with on-site Abelian symmetries or local constraints, focusing primarily on those with conserved dipole and higher moments. In the limit of large local Hilbert space dimension, we find that the spectral form factor $K(t)$ of Floquet random circuits can be mapped exactly to a classical Markov circuit, and, at late times, is related to the partition function of a frustration-free Rokhsar-Kivelson (RK) type Hamiltonian. Through this mapping, we show that the inverse of the spectral gap of the RK-Hamiltonian lower bounds the Thouless time $t_{\mathrm{Th}}$ of the underlying circuit. For systems with conserved higher moments, we derive a field theory for the corresponding RK-Hamiltonian by proposing a generalized height field representation for the Hilbert space of the effective spin chain. Using the field theory formulation, we obtain the dispersion of the low-lying excitations of the RK-Hamiltonian in the continuum limit, which allows us to extract $t_{\mathrm{Th}}$. In particular, we analytically argue that in a system of length $L$ that conserves the $m^{th}$ multipole moment, $t_{\mathrm{Th}}$ scales subdiffusively as $L^{2(m+1)}$. We also show that our formalism directly generalizes to higher dimensional circuits, and that in systems that conserve any component of the $m^{th}$ multipole moment, $t_{\mathrm{Th}}$ has the same scaling with the linear size of the system. Our work therefore provides a general approach for studying spectral statistics in constrained many-body chaotic systems.

Related papers

• Slow Mixing of Quantum Gibbs Samplers [47.373245682678515]
  We present a quantum generalization of these tools through a generic bottleneck lemma. This lemma focuses on quantum measures of distance, analogous to the classical Hamming distance but rooted in uniquely quantum principles. Even with sublinear barriers, we use Feynman-Kac techniques to lift classical to quantum ones establishing tight lower bound $T_mathrmmix = 2Omega(nalpha)$.
  arXiv  Detail & Related papers  (2024-11-06T22:51:27Z)
• 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)
• Exact dynamics of quantum dissipative $XX$ models: Wannier-Stark localization in the fragmented operator space [49.1574468325115]
  We find an exceptional point at a critical dissipation strength that separates oscillating and non-oscillating decay. We also describe a different type of dissipation that leads to a single decay mode in the whole operator subspace.
  arXiv  Detail & Related papers  (2024-05-27T16:11:39Z)
• Boundary Chaos: Spectral Form Factor [0.0]
  Random matrix spectral correlations are a defining feature of quantum chaos. We study such correlations in a minimal model of chaotic many-body quantum dynamics. We find they coincide with random matrix theory, possibly after a non-zero Thouless time.
  arXiv  Detail & Related papers  (2023-12-14T11:28:43Z)
• Theory of free fermions under random projective measurements [43.04146484262759]
  We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers. We derive a non-linear sigma model (NLSM) as an effective field theory of the problem.
  arXiv  Detail & Related papers  (2023-04-06T15:19:33Z)
• Correspondence between open bosonic systems and stochastic differential equations [77.34726150561087]
  We show that there can also be an exact correspondence at finite $n$ when the bosonic system is generalized to include interactions with the environment. A particular system with the form of a discrete nonlinear Schr"odinger equation is analyzed in more detail.
  arXiv  Detail & Related papers  (2023-02-03T19:17:37Z)
• Continuous percolation in a Hilbert space for a large system of qubits [58.720142291102135]
  The percolation transition is defined through the appearance of the infinite cluster. We show that the exponentially increasing dimensionality of the Hilbert space makes its covering by finite-size hyperspheres inefficient. Our approach to the percolation transition in compact metric spaces may prove useful for its rigorous treatment in other contexts.
  arXiv  Detail & Related papers  (2022-10-15T13:53:21Z)
• Analyticity constraints bound the decay of the spectral form factor [0.0]
  Quantum chaos cannot develop faster than $lambda leq 2 pi/(hbar beta)$ for systems in thermal equilibrium. We show that similar constraints also bound the decay of the spectral form factor (SFF) The relation of the derived bound with other known bounds, including quantum speed limits, is discussed.
  arXiv  Detail & Related papers  (2022-02-23T19:00:00Z)
• Many-Body Quantum Chaos and Space-time Translational Invariance [0.0]
  We study the consequences of having translational invariance in space and in time in many-body quantum chaotic systems. We consider an ensemble of random quantum circuits, composed of single-site random unitaries and nearest neighbour couplings. We numerically demonstrate, with simulations of two distinct circuit models, that in such a scaling limit, most microscopic details become unimportant.
  arXiv  Detail & Related papers  (2021-09-09T18:00:00Z)
• Random Matrix Spectral Form Factor in Kicked Interacting Fermionic Chains [1.6295305195753724]
  We study quantum chaos and spectral correlations in periodically driven (Floquet) fermionic chains with long-range two-particle interactions. We analytically show that the spectral form factor precisely follows the prediction of random matrix theory in the regime of long chains.
  arXiv  Detail & Related papers  (2020-05-21T07:02:04Z)

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.