Signatures of rare states and thermalization in a theory with confinement

Journal Article · 06 May 2019 · Physical Review B

DOI: https://doi.org/10.1103/PhysRevB.99.195108 · OSTI ID:1529074

Robinson, Neil J. ^[1]; James, Andrew J. A. ^[2]; Konik, Robert M.  ^[3]

---

1. Univ. of Amsterdam, Amsterdam (The Netherlands)
2. The Open Univ., Milton Keynes (United Kingdom); Univ. College London, London (United Kingdom)
3. Brookhaven National Lab. (BNL), Upton, NY (United States)

There is a dichotomy in the nonequilibrium dynamics of quantum many-body systems. In the presence of integrability, expectation values of local operators equilibrate to values described by a generalized Gibbs ensemble, which retains extensive memory about the initial state of the system. On the other hand, in generic systems such expectation values relax to stationary values described by the thermal ensemble, fixed solely by the energy of the state. At the heart of understanding, this dichotomy is the eigenstate thermalization hypothesis (ETH): individual eigenstates in nonintegrable systems are thermal, in the sense that expectation values agree with the thermal prediction at a temperature set by the energy of the eigenstate. In systems where ETH is violated, thermalization can be avoided. Thus, establishing the range of validity of ETH is crucial in understanding whether a given quantum system thermalizes. Here, we study a simple model with confinement, the quantum Ising chain with a longitudinal field, in which ETH is violated. Despite an absence of integrability, there exist rare (nonthermal) states that persist far into the spectrum. These arise as a direct consequence of confinement: pairs of particles are confined, forming new “meson” excitations whose energy can be extensive in the system size. We show that such states are nonthermal in both the continuum and in the low-energy spectrum of the corresponding lattice model. Here, we highlight that the presence of such states within the spectrum has important consequences, with certain quenches leading to an absence of thermalization and local observables evolving anomalously.

• Research Organization: Brookhaven National Laboratory (BNL), Upton, NY (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
• Grant/Contract Number: SC0012704
• OSTI ID: 1529074
• Report Number(s): BNL--211781-2019-JAAM
• Journal Information: Physical Review B, Journal Name: Physical Review B Journal Issue: 19 Vol. 99; ISSN 2469-9950; ISSN PRBMDO
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English