Duality, Criticality, Anomaly, and Topology in Quantum Spin-1 Chains

• URL: http://arxiv.org/abs/2203.15791v3
• Date: Wed, 29 Mar 2023 17:09:12 GMT
• Title: Duality, Criticality, Anomaly, and Topology in Quantum Spin-1 Chains
• Authors: Hong Yang, Linhao Li, Kouichi Okunishi, Hosho Katsura
• Abstract summary: We argue that a model with self-duality (i.e., invariant under $U_textKT$) is natural to be at a critical or multicritical point. In particular, when $H$ is the Hamiltonian of the spin-1 antiferromagnetic Heisenberg chain, we prove that the self-dual model $H + U_textKT$ is exactly equivalent to a gapless spin-$1/2$ XY chain.
• Score: 15.795926248847026
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In quantum spin-1 chains, there is a nonlocal unitary transformation known as the Kennedy-Tasaki transformation $U_{\text{KT}}$, which defines a duality between the Haldane phase and the $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry-breaking phase. In this paper, we find that $U_{\text{KT}}$ also defines a duality between a topological Ising critical phase and a trivial Ising critical phase, which provides a "hidden symmetry breaking" interpretation for the topological criticality. Moreover, since the duality relates different phases of matter, we argue that a model with self-duality (i.e., invariant under $U_{\text{KT}}$) is natural to be at a critical or multicritical point. We study concrete examples to demonstrate this argument. In particular, when $H$ is the Hamiltonian of the spin-1 antiferromagnetic Heisenberg chain, we prove that the self-dual model $H + U_{\text{KT}} H U_{\text{KT}}$ is exactly equivalent to a gapless spin-$1/2$ XY chain, which also implies an emergent quantum anomaly. On the other hand, we show that the topological and trivial Ising criticalities that are dual to each other meet at a multicritical point which is indeed self-dual.

Related papers

• KPZ scaling from the Krylov space [83.88591755871734]
  Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang scaling in late-time correlators and autocorrelators has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis.
  arXiv  Detail & Related papers  (2024-06-04T20:57:59Z)
• Walking behavior induced by $\mathcal{PT}$ symmetry breaking in a non-Hermitian $\rm XY$ model with clock anisotropy [0.0]
  A quantum system governed by a non-Hermitian Hamiltonian may exhibit zero temperature phase transitions driven by interactions. We show that when the $mathcalPT$ symmetry is broken, and time-evolution becomes non-unitary, a scaling behavior similar to the Berezinskii-Kosterlitz-Thouless phase transition ensues.
  arXiv  Detail & Related papers  (2024-04-26T12:45:16Z)
• Tunable quantum criticality and pseudocriticality across the fixed-point annihilation in the anisotropic spin-boson model [0.26107298043931204]
  We study the nontrivial renormalization-group scenario of fixed-point annihilation in spin-boson models. We find a tunable transition between two localized phases that can be continuous or strongly first-order. We also find scaling behavior at the symmetry-enhanced first-order transition, for which the inverse correlation-length exponent is given by the bath exponent.
  arXiv  Detail & Related papers  (2024-03-04T19:00:07Z)
• Measurement-induced phase transition for free fermions above one dimension [46.176861415532095]
  Theory of the measurement-induced entanglement phase transition for free-fermion models in $d>1$ dimensions is developed. Critical point separates a gapless phase with $elld-1 ln ell$ scaling of the second cumulant of the particle number and of the entanglement entropy.
  arXiv  Detail & Related papers  (2023-09-21T18:11:04Z)
• Rigorous derivation of the Efimov effect in a simple model [68.8204255655161]
  We consider a system of three identical bosons in $mathbbR3$ with two-body zero-range interactions and a three-body hard-core repulsion of a given radius $a>0$.
  arXiv  Detail & Related papers  (2023-06-21T10:11:28Z)
• 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)
• Symmetry-protected topological phases, conformal criticalities, and duality in exactly solvable SO($n$) spin chains [0.0]
  We introduce a family of SO($n$)-symmetric spin chains which generalize the transverse-field Ising chain for $n=1$. Their phase diagrams include a critical point described by the $mathrmSpin(n)_1$ conformal field theory.
  arXiv  Detail & Related papers  (2023-05-05T09:47:11Z)
• A New Look at the $C^{0}$-formulation of the Strong Cosmic Censorship Conjecture [68.8204255655161]
  We argue that for generic black hole parameters as initial conditions for Einstein equations, the metric is $C0$-extendable to a larger Lorentzian manifold. We prove it violates the "complexity=volume" conjecture for a low-temperature hyperbolic AdS$_d+1$ black hole dual to a CFT living on a ($d-1$)-dimensional hyperboloid $H_d-1$.
  arXiv  Detail & Related papers  (2022-06-17T12:14:33Z)
• The Asymmetric Valence-Bond-Solid States in Quantum Spin Chains: The Difference Between Odd and Even Spins [0.0]
  We develop an intuitive diagrammatic explanation of the difference between chains with odd $S$ and even $S$. This is at the heart of the theory of symmetry-protected topological (SPT) phases. It also extends to spin chains with general integer $S$ and provides us with an explanation of the essential difference between models with odd and even spins.
  arXiv  Detail & Related papers  (2022-05-02T04:58:31Z)
• Quantum Many-Body Scars in Spin-1 Kitaev Chains [1.340610646365466]
  We study the many-body scars in the spin-1 Kitaev chain where the so-called PXP Hamiltonian is exactly embedded in the spectra. We find that the scarred state is stable for perturbations which obey $vertmathbbZ_krangle$, while it becomes unstable against Heisenberg-type perturbations.
  arXiv  Detail & Related papers  (2022-01-23T10:11:32Z)
• Boundary time crystals in collective $d$-level systems [64.76138964691705]
  Boundary time crystals are non-equilibrium phases of matter occurring in quantum systems in contact to an environment. We study BTC's in collective $d$-level systems, focusing in the cases with $d=2$, $3$ and $4$.
  arXiv  Detail & Related papers  (2021-02-05T19:00:45Z)

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.