Related papers: The spectrum of local random Hamiltonians

The spectrum of local random Hamiltonians

URL: http://arxiv.org/abs/2210.00855v1
Date: Fri, 30 Sep 2022 04:57:41 GMT
Title: The spectrum of local random Hamiltonians
Authors: Benoit Collins, Zhi Yin, Liang Zhao, Ping Zhong
Abstract summary: The spectrum of a local random Hamiltonian can be represented generically by the so-called $epsilon$-free convolution of its local terms' probability distributions. We establish an isomorphism between the set of $epsilon$-noncrossing partitions and permutations to study its spectrum.
Score: 8.628477174338016
License: http://creativecommons.org/licenses/by-nc-nd/4.0/
Abstract: The spectrum of a local random Hamiltonian can be represented generically by the so-called $\epsilon$-free convolution of its local terms' probability distributions. We establish an isomorphism between the set of $\epsilon$-noncrossing partitions and permutations to study its spectrum. Moreover, we derive some lower and upper bounds for the largest eigenvalue of the Hamiltonian.

Related papers

Asymptotic Gaussian Fluctuations of Eigenvectors in Spectral Clustering [24.558241146742205]
It is shown that the signal $+$ noise structure of a general spike random matrix model is transferred to the eigenvectors of the corresponding Gram kernel matrix. This CLT-like result was the last missing piece to precisely predict the classification performance of spectral clustering.
arXiv Detail & Related papers (2024-02-19T17:25:12Z)
Digitizing lattice gauge theories in the magnetic basis: reducing the breaking of the fundamental commutation relations [0.0]
We present a digitization scheme for the lattice $mathrmSU(2)$ gauge theory Hamiltonian in the $mathitmagnetic$ $mathitbasis$, where the gauge links are unitary and diagonal. The digitization is obtained from a particular partitioning of the $mathrmSU(2)$ group manifold, with the canonical momenta constructed by an approximation of the Lie derivatives on this partitioning.
arXiv Detail & Related papers (2023-11-20T17:11:20Z)
Random Lindblad operators obeying detailed balance [0.18899300124593646]
We introduce different ensembles of random Lindblad operators $cal L$, which satisfy quantum detailed balance condition with respect to the given stationary state $sigma$ of size $N$. We show that similar universal properties hold for the detailed balance-obeying Kolmogorov generators obtained by applying superdecoherence to an ensemble of random Davies generators.
arXiv Detail & Related papers (2023-04-06T09:38:16Z)
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)
Condition-number-independent Convergence Rate of Riemannian Hamiltonian Monte Carlo with Numerical Integrators [22.49731518828916]
We show that for distributions in the form of $e-alphatopx$ on a polytope with $m constraints, the convergence rate of a family of commonly-used$$ is independent of $leftVert alpharightVert$ and the geometry of the polytope. These guarantees are based on a general bound on the convergence rate for densities of the form $e-f(x)$ in terms of parameters of the manifold and the integrator.
arXiv Detail & Related papers (2022-10-13T17:46:51Z)
Spectra of generators of Markovian evolution in the thermodynamic limit: From non-Hermitian to full evolution via tridiagonal Laurent matrices [0.0]
We obtain a representation of the Lindbladian as a direct integral of finite range bi-infinite Laurent matrices with rank-$r$-perturbations. We prove gaplessness, absence of residual spectrum and a condition for convergence of finite volume spectra to their infinite volume counterparts.
arXiv Detail & Related papers (2022-06-20T16:32:14Z)
Symplectic tomographic probability distribution of crystallized Schr\"odinger cat states [1.2891210250935143]
We study a superposition of generic Gaussian states associated to symmetries of a regular polygon of n sides. We obtain the Wigner functions and tomographic probability distributions determining the density matrices of the states.
arXiv Detail & Related papers (2022-03-15T11:03:47Z)
Concentration of OTOC and Lieb-Robinson velocity in random Hamiltonians [0.0]
Commutator between operators at different space and time has been a diagnostic for locality of unitary evolution. In this work, we study commutators in typical Hamiltonians.
arXiv Detail & Related papers (2021-03-16T16:37:19Z)
Universal Approximation Property of Neural Ordinary Differential Equations [19.861764482790544]
We show that NODEs can form an $Lp$-universal approximator for continuous maps under certain conditions. We also show their stronger approximation property, namely the $sup$-universality for approximating a large class of diffeomorphisms.
arXiv Detail & Related papers (2020-12-04T05:53:21Z)
Quasi-symmetry groups and many-body scar dynamics [13.95461883391858]
In quantum systems, a subspace spanned by degenerate eigenvectors of the Hamiltonian may have higher symmetries than those of the Hamiltonian itself. When the group is a Lie group, an external field coupled to certain generators of the quasi-symmetry group lifts the degeneracy. We provide two related schemes for constructing one-dimensional spin models having on-demand quasi-symmetry groups.
arXiv Detail & Related papers (2020-07-20T18:05:21Z)

This list is automatically generated from the titles and abstracts of the papers in this site.