Thermalization and Its Absence within Krylov Subspaces of a Constrained Hamiltonian

By Sanjay Moudgalya, Abhinav Prem, R. Nandkishore, N. Regnault, Bogdan Andrei Bernevig. Memorial Volume for Shoucheng Zhang, 2019

170 citations recorded by the source corpus.

We study the quantum dynamics of a simple translation invariant, center-of-mass (CoM) preserving model of interacting fermions in one dimension (1D), which arises in multiple experimentally realizable contexts. We show that this model naturally displays the phenomenology associated with fractonic systems, wherein single charges can only move by emitting dipoles. This allows us to demonstrate the rich Krylov fractured structure of this model, whose Hilbert space shatters into exponentially many dynamically disconnected subspaces. Focusing on exponentially large Krylov subspaces, we show that these can be either be integrable or non-integrable, thereby establishing the notion of Krylov-restricted thermalization. We analytically find a tower of integrable Krylov subspaces of this Hamiltonian, all of which map onto spin-1/2 XX models of various system sizes. We also discuss the physics of the non-integrable subspaces, where we show evidence for weak Eigenstate Thermalization Hypothesis (ETH) restricted to each non-integrable Krylov subspace. Further, we show that constraints in some of the thermal Krylov subspaces cause the long-time expectation values of local operators to deviate from behavior typically expected from translation-invariant systems. Finally, we show using a Schrieffer-Wolff transformation that such models naturally appear as effective Hamiltonians in the large electric field limit of the interacting Wannier-Stark problem, and comment on connections of our work with the phenomenon of Bloch many-body localization.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/02679e3ab2439a081978f0d4414166e419c889ec

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In Atomic and Molecular Physics, and Optics

1. V. Khemani
2. R. Nandkishore
3. M. Pretko
4. D. Abanin
5. A. Gromov
6. Maksym Serbyn
7. Yizhi You
8. Anushya Chandran

Citations in the corpus

• Fracton phases of matter (2020, background): “[113] Sanjay Moudgalya, Abhinav Prem, Rahul Nandkishore, Nicolas Regnault, and B.”
• Quantum many-body scars and weak breaking of ergodicity (2020, background): “This causes a dynamical “fracture” of the Hilbert space in the sense that the Schrödinger dynamics initialized in any state |ψ〉 ∈ K must remain within the same subspace at any later time, exp(− i ~ tH)|ψ〉 ∈ K, hence the name “Krylov restricted thermalization” [62].”
• Fracton hydrodynamics (2020, background): “[42] Sanjay Moudgalya, Abhinav Prem, Rahul Nandkishore, Nicolas Regnault, and B.”
• Quantum Many-Body Scars: A Quasiparticle Perspective (2022, background): “In the cases of most interest, the states |ψ0〉 are simple experimentally preparable states (such as product states), and the dimension of K is a vanishing fraction of the full Hilbert space dimension, leading to “Krylov restricted thermalization” within K (103); in certain cases, the dynamics in K m”