Rigorous lower bound of dynamic critical exponents in critical frustration-free systems

• URL: http://arxiv.org/abs/2406.06415v1
• Date: Mon, 10 Jun 2024 16:08:33 GMT
• Title: Rigorous lower bound of dynamic critical exponents in critical frustration-free systems
• Authors: Rintaro Masaoka, Tomohiro Soejima, Haruki Watanabe,
• Abstract summary: We prove a rigorous lower bound $z geq 2$ for frustration-free Hamiltonians on any lattice in any spatial dimension. This bound applies to representative classes of frustration-free Hamiltonians.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The dynamic critical exponent $z$ characterizes the finite-size gap in gapless quantum many-body systems. We establish a rigorous lower bound $z \geq 2$ for frustration-free Hamiltonians on any lattice in any spatial dimension, given that their ground state exhibits a power-law decaying correlation function. This bound applies to representative classes of frustration-free Hamiltonians, including Rokhsar-Kivelson Hamiltonians, which are in one-to-one correspondence to Markov chains with locality, as well as parent Hamiltonians of critical projected entangled pair states with either a unique ground state or topologically degenerate ground states, and Hamiltonians with a plane-wave ground state.

Related papers

• Complexity of geometrically local stoquastic Hamiltonians [1.474723404975345]
  The QMA-completeness of the local Hamiltonian problem is a landmark result of the field of Hamiltonian complexity. We show that both the two- and one-dimensional geometrically local analogues remain MA-hard with high enough qudit dimension.
  arXiv  Detail & Related papers  (2024-07-22T09:27:25Z)
• 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)
• $W$ state is not the unique ground state of any local Hamiltonian [0.0]
  characterization of ground states among all quantum states is an important problem in quantum many-body physics. We introduce a new class of simple states, including the $W$ state, that can only occur as a ground state alongside an exactly degenerate partner.
  arXiv  Detail & Related papers  (2023-10-16T18:00:01Z)
• Theory of robust quantum many-body scars in long-range interacting systems [0.0]
  Quantum many-body scars (QMBS) are exceptional energy eigenstates of quantum many-body systems. We show that long-range interacting quantum spin systems generically host robust QMBS. Our theory unveils the stability mechanism of such QMBS for arbitrary system size.
  arXiv  Detail & Related papers  (2023-09-21T22:00:40Z)
• 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)
• Observing super-quantum correlations across the exceptional point in a single, two-level trapped ion [48.7576911714538]
  In two-level quantum systems - qubits - unitary dynamics theoretically limit these quantum correlations to $2qrt2$ or 1.5 respectively. Here, using a dissipative, trapped $40$Ca$+$ ion governed by a two-level, non-Hermitian Hamiltonian, we observe correlation values up to 1.703(4) for the Leggett-Garg parameter $K_3$. These excesses occur across the exceptional point of the parity-time symmetric Hamiltonian responsible for the qubit's non-unitary, coherent dynamics.
  arXiv  Detail & Related papers  (2023-04-24T19:44:41Z)
• The Negativity Hamiltonian: An operator characterization of mixed-state entanglement [0.0]
  We study the structure of the negativity Hamiltonian for fermionic conformal field theories and a free fermion chain. In both cases, we show that the negativity Hamiltonian assumes a quasi-local functional form, that is captured by simple functional relations.
  arXiv  Detail & Related papers  (2022-01-11T15:08:41Z)
• Spectrum of localized states in fermionic chains with defect and adiabatic charge pumping [68.8204255655161]
  We study the localized states of a generic quadratic fermionic chain with finite-range couplings. We analyze the robustness of the connection between bands against perturbations of the Hamiltonian.
  arXiv  Detail & Related papers  (2021-07-20T18:44:06Z)
• Non-equilibrium stationary states of quantum non-Hermitian lattice models [68.8204255655161]
  We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner. We focus on the quantum steady states of such models for both fermionic and bosonic systems.
  arXiv  Detail & Related papers  (2021-03-02T18:56:44Z)
• Entanglement Hamiltonian of Interacting Systems: Local Temperature Approximation and Beyond [0.0]
  We investigate the second quantization form of the entanglement Hamiltonian of various subregions for the ground-state of lattice fermions and spin models. The relation between the EH and the model Hamiltonian itself is an unsolved problem for the ground-state of generic local Hamiltonians.
  arXiv  Detail & Related papers  (2020-12-09T19:00:02Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)

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.