Related papers: Quadratic dispersion relations in gapless frustration-free systems

Quadratic dispersion relations in gapless frustration-free systems

URL: http://arxiv.org/abs/2406.06414v1
Date: Mon, 10 Jun 2024 16:08:31 GMT
Title: Quadratic dispersion relations in gapless frustration-free systems
Authors: Rintaro Masaoka, Tomohiro Soejima, Haruki Watanabe,
Abstract summary: We argue that the dispersion of low energy excitations in gapless frustration-free Hamiltonians is actually a general property of such systems. This may be understood as a no-go theorem realizing gapless phases with linearly dispersive excitations in frustration-free Hamiltonians.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: Recent case-by-case studies revealed that the dispersion of low energy excitations in gapless frustration-free Hamiltonians is often quadratic or softer. In this work, we argue that this is actually a general property of such systems. By combining a previous study by Bravyi and Gosset and the min-max principle, we prove this hypothesis for models with local Hilbert spaces of dimension two that contains only nearest-neighbor interactions on cubic lattice. This may be understood as a no-go theorem realizing gapless phases with linearly dispersive excitations in frustration-free Hamiltonians. We also provide examples of frustration-free Hamiltonians in which the plane-wave state of a single spin flip does not constitute low energy excitations.

Related papers

Rigorous lower bound of dynamic critical exponents in critical frustration-free systems [0.0]
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.
arXiv Detail & Related papers (2024-06-10T16:08:33Z)
Quantized Thouless pumps protected by interactions in dimerized Rydberg tweezer arrays [41.94295877935867]
In the noninteracting case, quantized Thouless pumps can only occur when a topological singularity is encircled adiabatically. In the presence of interactions, such topological transport can even persist for exotic paths in which the system gets arbitrarily close to the noninteracting singularity.
arXiv Detail & Related papers (2024-02-14T16:58:21Z)
Local quenches in fracton field theory: Lieb-Robinson bound, non-causal dynamics and fractal excitation patterns [37.69303106863453]
We study the out-of-equilibrium dynamics induced by a local perturbation in fracton field theory. For the theory in finite volume, we show that the fracton wave front acquires fractal shape with non-trivial Hausdorff dimension.
arXiv Detail & Related papers (2023-10-17T12:21:15Z)
A new look at the theory of point interactions [0.0]
We investigate the entire family of multi-center point interaction Hamiltonians. We show that a large sub-family of these operators do not become either singular or trivial when the positions of two or more scattering centers tend to coincide.
arXiv Detail & Related papers (2023-06-17T08:23:55Z)
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)
In-Gap Band Formation in a Periodically Driven Charge Density Wave Insulator [68.8204255655161]
Periodically driven quantum many-body systems host unconventional behavior not realized at equilibrium. We investigate such a setup for strongly interacting spinless fermions on a chain, which at zero temperature and strong interactions form a charge density wave insulator.
arXiv Detail & Related papers (2022-05-19T13:28:47Z)
Spectral form factor in a minimal bosonic model of many-body quantum chaos [1.3793594968500609]
We study spectral form factor in periodically-kicked bosonic chains. We numerically find a nontrivial systematic system-size dependence of the Thouless time.
arXiv Detail & Related papers (2022-03-10T15:56:24Z)
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)
Chaos and subdiffusion in the infinite-range coupled quantum kicked rotors [0.0]
We map the infinite-range coupled quantum kicked rotors over an infinite-range coupled interacting bosonic model. In the thermodynamic limit the system is described by a set of coupled Gross-Pitaevskij equations equivalent to an effective nonlinear single-rotor Hamiltonian.
arXiv Detail & Related papers (2021-02-15T22:29:01Z)
Frustration-induced emergent Hilbert space fragmentation [0.9453554184019105]
Lattice geometry and quantum mechanics can conspire to produce constrained quantum dynamics and associated glassy behavior. We study their level statistics and relaxation dynamics to develop a coherent picture of fragmentation in various limits of the XXZ model on the kagome lattice.
arXiv Detail & Related papers (2020-11-03T19:00:01Z)
On the complex behaviour of the density in composite quantum systems [62.997667081978825]
We study how the probability of presence of a particle is distributed between the two parts of a composite fermionic system. We prove that it is a non-perturbative property and we find out a large/small coupling constant duality. Inspired by the proof of KAM theorem, we are able to deal with this problem by introducing a cut-off in energies that eliminates these small denominators.
arXiv Detail & Related papers (2020-04-14T21:41:15Z)

This list is automatically generated from the titles and abstracts of the papers in this site.