Skeleton of Matrix-Product-State-Solvable Models Connecting Topological Phases of Matter

• URL: http://arxiv.org/abs/2105.12143v2
• Date: Fri, 29 Oct 2021 09:39:23 GMT
• Title: Skeleton of Matrix-Product-State-Solvable Models Connecting Topological Phases of Matter
• Authors: Nick G. Jones, Julian Bibo, Bernhard Jobst, Frank Pollmann, Adam Smith, Ruben Verresen
• Abstract summary: We study the one-dimensional BDI class -- non-acting spinless fermions with time-reversal. This class contains the Kitaev chain and is Jordan-Wignerdual to various symmetry-breaking and symmetry-protected spin chains. We provide an explicit construction of the ground state MPS, its bond dimension growing with the range of the Hamiltonian.
• Score: 0.39146761527401414
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Models whose ground states can be written as an exact matrix product state (MPS) provide valuable insights into phases of matter. While MPS-solvable models are typically studied as isolated points in a phase diagram, they can belong to a connected network of MPS-solvable models, which we call the MPS skeleton. As a case study where we can completely unearth this skeleton, we focus on the one-dimensional BDI class -- non-interacting spinless fermions with time-reversal symmetry. This class, labelled by a topological winding number, contains the Kitaev chain and is Jordan-Wigner-dual to various symmetry-breaking and symmetry-protected topological (SPT) spin chains. We show that one can read off from the Hamiltonian whether its ground state is an MPS: defining a polynomial whose coefficients are the Hamiltonian parameters, MPS-solvability corresponds to this polynomial being a perfect square. We provide an explicit construction of the ground state MPS, its bond dimension growing exponentially with the range of the Hamiltonian. This complete characterization of the MPS skeleton in parameter space has three significant consequences: (i) any two topologically distinct phases in this class admit a path of MPS-solvable models between them, including the phase transition which obeys an area law for its entanglement entropy; (ii) we illustrate that the subset of MPS-solvable models is dense in this class by constructing a sequence of MPS-solvable models which converge to the Kitaev chain (equivalently, the quantum Ising chain in a transverse field); (iii) a subset of these MPS states can be particularly efficiently processed on a noisy intermediate-scale quantum computer.

Related papers

• Strong and weak symmetries and their spontaneous symmetry breaking in mixed states emerging from the quantum Ising model under multiple decoherence [0.0]
  We study phenomena generated by interplay between two types of decoherence applied to the one-dimensional transverse field Ising model (TFIM) We find various types of mixed states emergent from the ground states of the TFIM. In that study, strong and weak $Z$ symmetries play an important role, for which we introduce efficient order parameters.
  arXiv  Detail & Related papers  (2024-12-17T10:00:29Z)
• Hilbert space geometry and quantum chaos [39.58317527488534]
  We consider the symmetric part of the QGT for various multi-parametric random matrix Hamiltonians. We find for a two-dimensional parameter space that, while the ergodic phase corresponds to the smooth manifold, the integrable limit marks itself as a singular geometry with a conical defect.
  arXiv  Detail & Related papers  (2024-11-18T19:00:17Z)
• Cavity Control of Topological Qubits: Fusion Rule, Anyon Braiding and Majorana-Schrödinger Cat States [39.58317527488534]
  We investigate the impact of introducing a local cavity within the center of a topological chain. This cavity induces a scissor-like effect that bisects the chain, liberating Majorana zero modes (MZMs) within the bulk. By leveraging the symmetry properties of fermion modes within a two-site cavity, we propose a novel method for generating MZM-polariton Schr"odinger cat states.
  arXiv  Detail & Related papers  (2024-09-06T18:00:00Z)
• Theory of free fermions dynamics under partial post-selected monitoring [49.1574468325115]
  We derive a partial post-selected Schrdinger"o equation based on a microscopic description of continuous weak measurement. We show that the passage to the monitored universality occurs abruptly at finite partial post-selection. Our approach establishes a way to study MiPTs for arbitrary subsets of quantum trajectories.
  arXiv  Detail & Related papers  (2023-12-21T16:53:42Z)
• Emergent Topology in Many-Body Dissipative Quantum Matter [0.0]
  We study the dissipative dynamics of pseudo-Hermitian many-body quantum systems. We find the same topological features for a wide range of parameters suggesting that they are universal. In the limit of weak coupling to the bath, topological modes govern the approach to equilibrium.
  arXiv  Detail & Related papers  (2023-11-24T18:15:22Z)
• Symmetry-Preserving Quadratic Lindbladian and Dissipation Driven Topological Transitions in Gaussian States [5.072946612096282]
  We characterize the density matrix topology by the topological invariant of its modular Hamiltonian. We present two examples of dissipation-driven topological transitions where the modular Hamiltonian lies in the AIII class with U(1) symmetry and the DIII class without U(1) symmetry.
  arXiv  Detail & Related papers  (2023-01-11T07:52:00Z)
• Boundary conditions dependence of the phase transition in the quantum Newman-Moore model [0.0]
  We study the triangular plaquette model (TPM) in the presence of a transverse magnetic field on a lattice with periodic boundaries in both spatial dimensions. We consider specifically the approach to the ground state phase transition of this quantum TPM as a function of the system size and type of boundary conditions.
  arXiv  Detail & Related papers  (2023-01-07T11:00:47Z)
• Quantum correlations, entanglement spectrum and coherence of two-particle reduced density matrix in the Extended Hubbard Model [62.997667081978825]
  We study the ground state properties of the one-dimensional extended Hubbard model at half-filling. In particular, in the superconducting region, we obtain that the entanglement spectrum signals a transition between a dominant singlet (SS) to triplet (TS) pairing ordering in the system.
  arXiv  Detail & Related papers  (2021-10-29T21:02:24Z)
• Non-Markovian Stochastic Schr\"odinger Equation: Matrix Product State Approach to the Hierarchy of Pure States [65.25197248984445]
  We derive a hierarchy of matrix product states (HOMPS) for non-Markovian dynamics in open finite temperature. The validity and efficiency of HOMPS is demonstrated for the spin-boson model and long chains where each site is coupled to a structured, strongly non-Markovian environment.
  arXiv  Detail & Related papers  (2021-09-14T01:47:30Z)
• The quantum phase transitions of dimer chain driven by an imaginary ac field [0.0]
  A topologically equivalent tight binding model is proposed to study the quantum phase transitions of dimer chain driven by an imaginary ac field. The approach has the potential applications to investigate the topological states of matter driven by the complex external parameters.
  arXiv  Detail & Related papers  (2020-09-08T09:07:45Z)
• 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.