Non-zero momentum requires long-range entanglement

• URL: http://arxiv.org/abs/2112.06946v2
• Date: Tue, 31 May 2022 18:04:51 GMT
• Title: Non-zero momentum requires long-range entanglement
• Authors: Lei Gioia, Chong Wang
• Abstract summary: We show that a quantum state in a lattice spin (boson) system must be long-range entangled if it has non-zero lattice momentum. The statement can also be generalized to fermion systems.
• Score: 6.018940870331878
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We show that a quantum state in a lattice spin (boson) system must be long-range entangled if it has non-zero lattice momentum, i.e. if it is an eigenstate of the translation symmetry with eigenvalue $e^{iP}\neq1$. Equivalently, any state that can be connected with a non-zero momentum state through a finite-depth local unitary transformation must also be long-range entangled. The statement can also be generalized to fermion systems. Some non-trivial consequences follow immediately from our theorem: (1) several different types of Lieb-Schultz-Mattis-Oshikawa-Hastings (LSMOH) theorems, including a previously unknown version involving only a discrete $\mathbb{Z}_n$ symmetry, can be derived in a simple manner from our result; (2) a gapped topological order (in space dimension $d>1$) must weakly break translation symmetry if one of its ground states on torus has nontrivial momentum - this generalizes the familiar physics of Tao-Thouless; (3) our result provides further evidence of the "smoothness" assumption widely used in the classification of crystalline symmetry-protected topological (cSPT) phases.

Related papers

• Exactly solvable models for fermionic symmetry-enriched topological phases and fermionic 't Hooft anomaly [33.49184078479579]
  The interplay between symmetry and topological properties plays a very important role in modern physics. How to realize all these fermionic SET (fSET) phases in lattice models remains to be a difficult open problem.
  arXiv  Detail & Related papers  (2024-10-24T19:52:27Z)
• Conformal geometry from entanglement [14.735587711294299]
  We identify a quantum information-theoretic mechanism by which the conformal geometry emerges at the gapless edge of a 2+1D quantum many-body system. We show that stationarity of $mathfrakc_mathrmtot$ is equivalent to a vector fixed-point equation involving $eta$, making our assumption locally checkable.
  arXiv  Detail & Related papers  (2024-04-04T18:00:03Z)
• Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
  We show how to reduce the geometry of degenerate states to the non-abelian connection $A$. We find independent invariants associated with each triple of subspaces. Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
  arXiv  Detail & Related papers  (2024-04-04T06:39:28Z)
• Anomaly in open quantum systems and its implications on mixed-state quantum phases [6.356631694532754]
  We develop a systematic approach to characterize the 't Hooft anomaly in open quantum systems. By representing their symmetry transformation through superoperators, we incorporate them in a unified framework. We find that anomalies of bosonic systems are classified by $Hd+2(Ktimes G,U(1))/Hd+2(G,U(1))$ in $d$ spatial dimensions.
  arXiv  Detail & Related papers  (2024-03-21T16:34:37Z)
• Symmetry-restricted quantum circuits are still well-behaved [45.89137831674385]
  We show that quantum circuits restricted by a symmetry inherit the properties of the whole special unitary group $SU(2n)$. It extends prior work on symmetric states to the operators and shows that the operator space follows the same structure as the state space.
  arXiv  Detail & Related papers  (2024-02-26T06:23:39Z)
• Entanglement asymmetry in the ordered phase of many-body systems: the Ising Field Theory [0.0]
  Global symmetries of quantum many-body systems can be spontaneously broken. In this study, we examine the entanglement asymmetry of a specific region. We also establish a field theoretic framework in the replica theory using twist operators.
  arXiv  Detail & Related papers  (2023-07-22T17:07:56Z)
• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum [77.34726150561087]
  We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians. We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-18T09:26:02Z)
• Ground state degeneracy on torus in a family of $\mathbb{Z}_N$ toric code [2.7286395031146062]
  Topologically ordered phases in $2+1$ dimensions are characterized by three mutually-related features. The most remarkable feature of the topologically ordered phases is that the ground state may be unique. We argue that this behavior originates from the nontrivial action of translations permuting anyon species.
  arXiv  Detail & Related papers  (2022-11-01T06:34:53Z)
• Non-perturbative constraints from symmetry and chirality on Majorana zero modes and defect quantum numbers in (2+1)D [0.0]
  In (1)D topological phases, unpaired Majorana zero modes (MZMs) can arise only if the internal symmetry group $G_f$ of the ground state splits as $G_f = G_b times mathbbZf$. In contrast, (2+1)D topological superconductors (TSC) can host unpaired MZMs at defects even when $G_f$ is not of the form $G_b times mathbbZf$.
  arXiv  Detail & Related papers  (2022-10-05T18:00:00Z)
• Non-Hermitian $C_{NH} = 2$ Chern insulator protected by generalized rotational symmetry [85.36456486475119]
  A non-Hermitian system is protected by the generalized rotational symmetry $H+=UHU+$ of the system. Our finding paves the way towards novel non-Hermitian topological systems characterized by large values of topological invariants.
  arXiv  Detail & Related papers  (2021-11-24T15:50:22Z)
• $\PT$ Symmetry and Renormalisation in Quantum Field Theory [62.997667081978825]
  Quantum systems governed by non-Hermitian Hamiltonians with $PT$ symmetry are special in having real energy eigenvalues bounded below and unitary time evolution. We show how $PT$ symmetry may allow interpretations that evade ghosts and instabilities present in an interpretation of the theory within a Hermitian framework.
  arXiv  Detail & Related papers  (2021-03-27T09:46:36Z)

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.