Flat-band induced local Hilbert space fragmentation

• URL: http://arxiv.org/abs/2306.15660v1
• Date: Tue, 27 Jun 2023 17:55:04 GMT
• Title: Flat-band induced local Hilbert space fragmentation
• Authors: Eul\`alia Nicolau, Anselmo M. Marques, Ricardo G. Dias, and Ver\`onica Ahufinger
• Abstract summary: We show that a class of flat-band lattices with underlying commutative local symmetries exhibit a locally fragmented Hilbert space. We analyze the fragmentation of the one-dimensional Pyrochlore chain, which exhibits both nonintegrable sectors, effective single-particle sectors, and frozen states.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We demonstrate that a complete class of flat-band lattices with underlying commutative local symmetries exhibit a locally fragmented Hilbert space. The equitable partition theorem ensures distinct parities for the compact localized states (CLSs) present in this class of flat-band lattices and the extended eigenstates of the system. In the presence of on-site bosonic interactions, such models exhibit a conserved quantity, the parity of the number of particles located in all the CLSs in a unit cell. As a consequence, the Hilbert space presents local fragmentation, which is only revealed upon rotating the basis of the Hamiltonian that decouples the CLSs at the single-particle level. We find that the fragmentation is strong and also robust to the addition of long-range interactions. As an example, we numerically analyze the fragmentation of the one-dimensional Pyrochlore chain, which exhibits both nonintegrable sectors, effective single-particle sectors, and frozen states. We also show that the entanglement entropies form a nested-dome structure typical of these fragmented systems and that thermalization is restricted to each sub-sector.

Related papers

• Quantum Fragmentation in the Extended Quantum Breakdown Model [0.0]
  We analytically show that, in the absence of any magnetic field for the spins, the model exhibits Hilbert space fragmentation into exponentially many Krylov subspaces. We also study the long-time behavior of the entanglement entropy and its deviation from the expected Page value as a probe of ergodicity in the system.
  arXiv  Detail & Related papers  (2024-01-29T19:00:10Z)
• Hilbert space fragmentation in a long-range system [0.0]
  We study the role of the interaction range on the Hilbert space fragmentation and many-body scar states. We show that both scar states and weak fragmentation of the Hilbert space survive for almost any range of the coupling.
  arXiv  Detail & Related papers  (2023-02-22T22:31:15Z)
• Fermion production at the boundary of an expanding universe: a cold-atom gravitational analogue [68.8204255655161]
  We study the phenomenon of cosmological particle production of Dirac fermions in a Friedman-Robertson-Walker spacetime. We present a scheme for the quantum simulation of this gravitational analogue by means of ultra-cold atoms in Raman optical lattices.
  arXiv  Detail & Related papers  (2022-12-02T18:28:23Z)
• Spectral response of disorder-free localized lattice gauge theories [0.22940141855172028]
  We show that certain lattice gauge theories exhibiting disorder-free localization have a characteristic response in spatially averaged spectral functions. We also show that local spectral functions of large finite clusters host discrete peaks whose positions agree with our analytical estimates.
  arXiv  Detail & Related papers  (2022-11-25T19:00:01Z)
• Multibody expansion of the local integrals of motion: How many pairs of particle-hole do we really need to describe the quasiparticles in the many-body localized phase? [0.0]
  We present a one-dimensional XXZ spin-$frac12$ Heisenberg chain in the presence of a random field and try to quantify the corrections needed to be considered in the picture of quasiparticles associated with LIOMs. We analytically obtain the coefficients of this expansion and discuss the effect of higher-order corrections associated with different numbers of particle-hole excitations.
  arXiv  Detail & Related papers  (2022-10-29T14:10:24Z)
• Localization in the random XXZ quantum spin chain [55.2480439325792]
  We study the many-body localization (MBL) properties of the Heisenberg XXZ spin-$frac12$ chain in a random magnetic field. We prove that the system exhibits localization in any given energy interval at the bottom of the spectrum in a nontrivial region of the parameter space.
  arXiv  Detail & Related papers  (2022-10-26T17:25:13Z)
• Continuous percolation in a Hilbert space for a large system of qubits [58.720142291102135]
  The percolation transition is defined through the appearance of the infinite cluster. We show that the exponentially increasing dimensionality of the Hilbert space makes its covering by finite-size hyperspheres inefficient. Our approach to the percolation transition in compact metric spaces may prove useful for its rigorous treatment in other contexts.
  arXiv  Detail & Related papers  (2022-10-15T13:53:21Z)
• Exact thermal properties of free-fermionic spin chains [68.8204255655161]
  We focus on spin chain models that admit a description in terms of free fermions. Errors stemming from the ubiquitous approximation are identified in the neighborhood of the critical point at low temperatures.
  arXiv  Detail & Related papers  (2021-03-30T13:15:44Z)
• Quantum particle across Grushin singularity [77.34726150561087]
  We study the phenomenon of transmission across the singularity that separates the two half-cylinders. All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection. This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
  arXiv  Detail & Related papers  (2020-11-27T12:53:23Z)
• Integrability of $1D$ Lindbladians from operator-space fragmentation [0.0]
  We introduce families of one-dimensional Lindblad equations describing open many-particle quantum systems. We show that Lindbladians featuring integrable operator-space fragmentation can be found in spin chains with arbitrary local physical dimension.
  arXiv  Detail & Related papers  (2020-09-24T15:10:43Z)
• Dynamical solitons and boson fractionalization in cold-atom topological insulators [110.83289076967895]
  We study the $mathbbZ$ Bose-Hubbard model at incommensurate densities. We show how defects in the $mathbbZ$ field can appear in the ground state, connecting different sectors. Using a pumping argument, we show that it survives also for finite interactions.
  arXiv  Detail & Related papers  (2020-03-24T17:31:34Z)

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.