Lieb-Schultz-Mattis Theorem in Open Quantum Systems
ORAL
Abstract
The Lieb-Schultz-Mattis (LSM) theorem provides a general constraint on quantum many-body systems and plays a significant role in the Haldane gap phenomena and topological phases of matter. Here, we extend the LSM theorem to open quantum systems and establish a general theorem that restricts the steady state and spectral gap of Liouvillians based solely on symmetry. Specifically, we demonstrate that the unique gapped steady state is prohibited when translation invariance and U(1) symmetry are simultaneously present for noninteger filling numbers. As an illustrative example, we find that no dissipative gap is open in the spin-1/2 dissipative Heisenberg model while a dissipative gap can be open in the spin-1 counterpart---an analog of the Haldane gap phenomena in open quantum systems. Furthermore, we show that the LSM constraint manifests itself in a quantum anomaly of the dissipative form factor of Liouvillians. We also find the LSM constraints due to symmetry intrinsic to open quantum systems, such as Kubo-Martin-Schwinger symmetry.
* K.K. is supported by the Japan Society for the Promotion of Science (JSPS) through the Overseas Research Fellowship. S.R. is supported by the National Science Foundation under Award No. DMR-2001181, and by a Simons Investigator Grant from the Simons Foundation (Award No. 566116). This work is supported by the Gordon and Betty Moore Foundation through Grant No. GBMF8685 toward the Princeton theory program.
–
Publication: arXiv:2305.16496
Presenters
-
Kohei Kawabata
Institute for Solid State Physics, University of Tokyo
Authors
-
Kohei Kawabata
Institute for Solid State Physics, University of Tokyo
-
Ramanjit Sohal
Princeton University
-
Shinsei Ryu
Princeton University