Weak universality, quantum many-body scars and anomalous infinite-temperature autocorrelations in a one-dimensional spin model with duality

• URL: http://arxiv.org/abs/2307.11161v4
• Date: Thu, 4 Jan 2024 09:28:13 GMT
• Title: Weak universality, quantum many-body scars and anomalous infinite-temperature autocorrelations in a one-dimensional spin model with duality
• Authors: Adithi Udupa, Samudra Sur, Sourav Nandy, Arnab Sen, Diptiman Sen
• Abstract summary: We study a one-dimensional spin-$1/2$ model with three-spin interactions and a transverse magnetic field $h$. We compute the critical exponents $z$, $beta$, $gamma$ and $nu$, and the central charge $c$. For a system with periodic boundary conditions, there are an exponentially large number of exact mid-spectrum zero-energy eigenstates.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study a one-dimensional spin-$1/2$ model with three-spin interactions and a transverse magnetic field $h$. The model has a $Z_2 \times Z_2$ symmetry, and a duality between $h$ and $1/h$. The self-dual point at $h=1$ is a quantum critical point with a continuous phase transition. We compute the critical exponents $z$, $\beta$, $\gamma$ and $\nu$, and the central charge $c$ numerically using exact diagonalization (ED) for systems with periodic boundary conditions. We find that both $z$ and $c$ are equal to $1$, implying that the critical point is governed by a conformal field theory. The values obtained for $\beta/\nu$, $\gamma/\nu$, and $\nu$ from ED suggest that the model exhibits Ashkin-Teller criticality with an effective coupling that is intermediate between the four-state Potts model and two decoupled transverse field Ising models. An analysis on larger systems but with open boundaries using density-matrix renormalization group calculations, however, shows that the self-dual point may be in the same universality class as the four-state Potts model. An energy level spacing analysis shows that the model is not integrable. For a system with periodic boundary conditions, there are an exponentially large number of exact mid-spectrum zero-energy eigenstates. A subset of these eigenstates have wave functions which are independent of $h$ and have unusual entanglement structure, suggesting that they are quantum many-body scars. The number of such states scales at least linearly with system size. Finally, we study the infinite-temperature autocorrelation functions close to one end of an open system. We find that some of the autocorrelators relax anomalously in time, with pronounced oscillations and very small decay rates if $h \gg 1$ or $h \ll 1$. If $h$ is close to the critical point, the autocorrelators decay quickly to zero except for an autocorrelator at the end site.

Related papers

• Slow Mixing of Quantum Gibbs Samplers [47.373245682678515]
  We present a quantum generalization of these tools through a generic bottleneck lemma. This lemma focuses on quantum measures of distance, analogous to the classical Hamming distance but rooted in uniquely quantum principles. Even with sublinear barriers, we use Feynman-Kac techniques to lift classical to quantum ones establishing tight lower bound $T_mathrmmix = 2Omega(nalpha)$.
  arXiv  Detail & Related papers  (2024-11-06T22:51:27Z)
• Gapped and gapless quantum spin liquids on the ruby lattice [0.0]
  We present a total of 50 U$bbZ(1) and 182 distinct states of ruby spin on mean-consistent structures. We also obtain a total of 64 anti-respecting space-group theories of spin on mean-consistent structures.
  arXiv  Detail & Related papers  (2024-09-24T18:00:00Z)
• Hamiltonians for Quantum Systems with Contact Interactions [49.1574468325115]
  We show that in the limit one obtains the one-body Hamiltonian for the light particle subject to $N$ (non-local) point interactions placed at fixed positions. We will verify that such non-local point interactions do not exhibit the ultraviolet pathologies that are present in the case of standard local point interactions.
  arXiv  Detail & Related papers  (2024-07-09T14:04:11Z)
• 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)
• 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)
• Localization measures of parity adapted U($D$)-spin coherent states applied to the phase space analysis of the $D$-level Lipkin-Meshkov-Glick model [0.0]
  We study phase-space properties of critical, parity symmetric, $N$-quDit systems undergoing a quantum phase transition. For finite $N$, parity can be restored by projecting DSCS onto $2D-1$ different parity invariant subspaces. Pres of the QPT are then visualized for finite $N$ by plotting the Husimi function of these parity projected DSCS in phase space.
  arXiv  Detail & Related papers  (2023-02-13T10:51:19Z)
• 3-body harmonic molecule [0.0]
  It governs the near-equilibrium $S$-states eigenfunctions $psi(r_12,r_13,r_23)$ of three identical point particles interacting by means of any pairwise confining potential $V(r_12,r_13,r_23)$ that entirely depends on the relative distances $r_ij=|mathbf r_i-mathbf r_j|$ between particles. The whole spectra of excited states is degenerate, and to analyze it a detailed
  arXiv  Detail & Related papers  (2022-08-18T16:44:07Z)
• Porter-Thomas fluctuations in complex quantum systems [0.0]
  We find that the coupling to the decay channels can change the effective number of degrees of freedom from $nu = 1$ to $nu = 2$. Our conclusions are based on a configuration-interaction Hamiltonian originally constructed to test the validity of transition-state theory.
  arXiv  Detail & Related papers  (2021-06-29T11:07:49Z)
• 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)
• Quantum Algorithms for Simulating the Lattice Schwinger Model [63.18141027763459]
  We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and fault-tolerant settings. In lattice units, we find a Schwinger model on $N/2$ physical sites with coupling constant $x-1/2$ and electric field cutoff $x-1/2Lambda$. We estimate observables which we cost in both the NISQ and fault-tolerant settings by assuming a simple target observable---the mean pair density.
  arXiv  Detail & Related papers  (2020-02-25T19:18:36Z)
• Anisotropy-mediated reentrant localization [62.997667081978825]
  We consider a 2d dipolar system, $d=2$, with the generalized dipole-dipole interaction $sim r-a$, and the power $a$ controlled experimentally in trapped-ion or Rydberg-atom systems. We show that the spatially homogeneous tilt $beta$ of the dipoles giving rise to the anisotropic dipole exchange leads to the non-trivial reentrant localization beyond the locator expansion.
  arXiv  Detail & Related papers  (2020-01-31T19:00:01Z)

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.