Lieb-Schultz-Mattis theorems and generalizations in long-range interacting systems

• URL: http://arxiv.org/abs/2405.14929v1
• Date: Thu, 23 May 2024 18:00:00 GMT
• Title: Lieb-Schultz-Mattis theorems and generalizations in long-range interacting systems
• Authors: Ruizhi Liu, Jinmin Yi, Shiyu Zhou, Liujun Zou,
• Abstract summary: We establish Lieb-Schultz-Mattis (LSM) theorems and their generalizations in systems with long-range interactions. We show that, for a quantum spin chain, if the interactions decay fast enough as their ranges increase and the Hamiltonian has an anomalous symmetry, the Hamiltonian cannot have a unique gapped symmetric ground state.
• Score: 3.988840381234705
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In a unified fashion, we establish Lieb-Schultz-Mattis (LSM) theorems and their generalizations in systems with long-range interactions. We show that, for a quantum spin chain, if the interactions decay fast enough as their ranges increase and the Hamiltonian has an anomalous symmetry, the Hamiltonian cannot have a unique gapped symmetric ground state. If the Hamiltonian contains only 2-spin interactions, these theorems hold when the interactions decay faster than $1/r^2$, with $r$ the distance between the two interacting spins. Moreover, any pure state with an anomalous symmetry, which may not be a ground state of any natural Hamiltonian, must be long-range entangled. The symmetries we consider include on-site internal symmetries combined with lattice translation symmetries, and they can also extend to purely internal but non-on-site symmetries. Moreover, these internal symmetries can be discrete or continuous. We explore the applications of the theorems through various examples.

Related papers

• Spontaneous symmetry breaking in open quantum systems: strong, weak, and strong-to-weak [4.41737598556146]
  We show that strong symmetry always spontaneously breaks into the corresponding weak symmetry. We conjecture that this relation among strong-to-weak symmetry breaking, gapless modes, and symmetry-charge diffusion is general for continuous symmetries.
  arXiv  Detail & Related papers  (2024-06-27T17:55:36Z)
• Quantifying non-Hermiticity using single- and many-particle quantum properties [14.37149160708975]
  The non-Hermitian paradigm of quantum systems displays salient features drastically different from Hermitian counterparts. We propose a formalism that quantifies the (dis-)similarity of these right and left ensembles, for single- as well as many-particle quantum properties. Our findings can be instrumental in unveiling new exotic quantum phases of non-Hermitian quantum many-body systems.
  arXiv  Detail & Related papers  (2024-06-19T13:04:47Z)
• Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders [37.69303106863453]
  We consider a system of interacting spinless fermions on a two-leg triangular ladder with $pi/2$ magnetic flux per triangular plaquette. Microscopically, the system exhibits a U(1) symmetry corresponding to the conservation of total fermionic charge, and a discrete $mathbbZ$ symmetry. At the intersection of the three phases, the system features a critical point with an emergent SU(2) symmetry.
  arXiv  Detail & Related papers  (2023-05-11T15:57:27Z)
• Quantum Mechanics as a Theory of Incompatible Symmetries [77.34726150561087]
  We show how classical probability theory can be extended to include any system with incompatible variables. We show that any probabilistic system (classical or quantal) that possesses incompatible variables will show not only uncertainty, but also interference in its probability patterns.
  arXiv  Detail & Related papers  (2022-05-31T16:04:59Z)
• Symmetry-induced decoherence-free subspaces [0.0]
  Preservation of coherence is a fundamental yet subtle phenomenon in open systems. We discriminate between local and global classes of decoherence-free subspaces for many-body systems. Poisson and Lie algebras play for symmetries in classical and quantum mechanics.
  arXiv  Detail & Related papers  (2022-05-20T10:05:14Z)
• Geometric approach to Lieb-Schultz-Mattis theorem without translation symmetry under inversion or rotation symmetry [6.737752058029072]
  We find that any inversion-symmetric spin system possesses a doubly degenerate spectrum when it hosts a half-integer spin at the inversion-symmetric point. We argue that these degeneracies imply that a symmetric unique gapped ground state that is smoothly connected to product states is forbidden in the original untwisted systems.
  arXiv  Detail & Related papers  (2021-10-17T13:36:51Z)
• Information retrieval and eigenstates coalescence in a non-Hermitian quantum system with anti-$\mathcal{PT}$ symmetry [15.273168396747495]
  Non-Hermitian systems with parity-time reversal ($mathcalPT$) or anti-$mathcalPT$ symmetry have attracted a wide range of interest owing to their unique characteristics and counterintuitive phenomena. We implement a Floquet Hamiltonian of a single qubit with anti-$mathcalPT$ symmetry by periodically driving a dissipative quantum system of a single trapped ion.
  arXiv  Detail & Related papers  (2021-07-27T07:11:32Z)
• Fermion and meson mass generation in non-Hermitian Nambu--Jona-Lasinio models [77.34726150561087]
  We investigate the effects of non-Hermiticity on interacting fermionic systems. We do this by including non-Hermitian bilinear terms into the 3+1 dimensional Nambu--Jona-Lasinio (NJL) model.
  arXiv  Detail & Related papers  (2021-02-02T13:56:11Z)
• Latent symmetry induced degeneracies [0.0]
  We develop an approach to explain degeneracies by tracing them back to symmetries of an isospectral effective Hamiltonian. As an application, we relate the degeneracies induced by the rotation symmetry of a real Hamiltonian to a non-abelian latent symmetry group.
  arXiv  Detail & Related papers  (2020-11-26T17:37:30Z)
• Equilibrium frame reveals hidden PT symmetry of passive systems [0.0]
  We show that non-Hermitian Hamiltonians possess hidden PT symmetries. We also show that the number of eigenstates having the same value in an exceptional point is usually smaller in the initial frame than in the equilibrium frame.
  arXiv  Detail & Related papers  (2020-08-14T18:28:37Z)
• 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.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.