The eigenstate thermalization hypothesis in constrained Hilbert spaces: A case study in non-Abelian anyon chains

Abstract

Many phases of matter, including superconductors, fractional quantum Hall fluids and spin liquids, are described by gauge theories with constrained Hilbert spaces. However, thermalization and the applicability of quantum statistical mechanics has primarily been studied in unconstrained Hilbert spaces. In this article, we investigate whether constrained Hilbert spaces permit local thermalization. Specifically, we explore whether the eigenstate thermalization hypothesis (ETH) holds in a pinned Fibonacci anyon chain, which serves as a representative case study. We first establish that the constrained Hilbert space admits a notion of locality, by showing that the influence of a measurement decays exponentially in space. This suggests that the constraints are no impediment to thermalization. We then provide numerical evidence that ETH holds for the diagonal and offdiagonal matrix elements of various local observables in a generic disorder-free non-integrable model. We also find that certain non-local observables obey ETH.

Eigenstate thermalization and quantum chaos in the Holstein polaron model

“…So far, the ETH has been verified for a wide number of lattice models such as nonintegrable spin-1/2 chains [23][24][25][26][27][28][29][30][31][32][33], ladders [26,[34][35][36] and square lattices [37][38][39], interacting spinless fermions [40,41], Bose-Hubbard [26,42] and Fermi-Hubbard chains [43], dipolar hard-core bosons [44], quantum dimer models [45] and Fibonacci anyons [46]. In these examples, mostly, direct two-body interactions in systems of either spins, fermions or bosons are responsible for rendering the system ergodic.…”

Eigenstate thermalization hypothesis in quantum dimer models

“…Our study of the 2D QDM combines a number of features that have proven to be of interest in other recent work on ETH [14][15][16][17][18]: First, it continues the progress of ETH studies from the familiar territory of 1D systems [19][20][21][22] into higher dimensions. Questions about ETH in systems in two or more dimensions, such as the transverse-field Ising model on the square lattice [14][15][16], are of great interest but challenging due to the rapid increase of the Hilbert-space dimension with system size.…”

“…To provide a more quantitative picture, we employ an approach that has proved useful in previous studies [14,17] by looking at fluctuations between the diagonal matrix elements in adjacent energy eigenstates. We first sort all the eigenstates by energy and then calculate the difference of diagonal matrix elements between adjacent eigenstates,…”

“…Second, the Hilbert space of the QDM is spanned by dimer configurations subject to strong local constraints. The study of ETH in constrained systems has recently been initiated by Chandran et al [17], who considered non-Abelian anyon chains, motivated by the question of whether the constraints can hinder thermalization.…”

Emergent Glassy Dynamics in a Quantum Dimer Model

“…Due to the Rydberg blockade [3][4][5][6][7][8][9][10], a constrained quantum manybody system is realized in which two excitations are forbidden to occupy neighboring lattice sites. Theoretical works have proposed a set of exceptional eigenstates, entitled "quantum many-body scars", and nearby integrable points to be responsible for the exotic quantum dynamics [11][12][13][14][15][16][17].…”