Bose-Fermi dualities for arbitrary one-dimensional quantum systems in the universal low energy regime

• URL: http://arxiv.org/abs/2009.00624v3
• Date: Sat, 17 Oct 2020 06:59:10 GMT
• Title: Bose-Fermi dualities for arbitrary one-dimensional quantum systems in the universal low energy regime
• Authors: Manuel Valiente
• Abstract summary: I consider general interacting systems of quantum particles in one spatial dimension. These consist of bosons or fermions, which can have any number of components, arbitrary spin or a combination thereof. The single-particle dispersion can be Galilean (non-relativistic), relativistic, or have any other form that may be relevant for the continuum limit of lattice theories.
• Score: 0.2741266294612775
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: I consider general interacting systems of quantum particles in one spatial dimension. These consist of bosons or fermions, which can have any number of components, arbitrary spin or a combination thereof, featuring low-energy two- and multiparticle interactions. The single-particle dispersion can be Galilean (non-relativistic), relativistic, or have any other form that may be relevant for the continuum limit of lattice theories. Using an algebra of generalized functions, statistical transmutation operators that are genuinely unitary are obtained, putting bosons and fermions in a one-to-one correspondence without the need for a short-distance hard core. In the non-relativistic case, low-energy interactions for bosons yield, order by order, fermionic dual interactions that correspond to the standard low-energy expansion for fermions. In this way, interacting fermions and bosons are fully equivalent to each other at low energies. While the Bose-Fermi mappings do not depend on microscopic details, the resulting statistical interactions heavily depend on the kinetic energy structure of the respective Hamiltonians. These statistical interactions are obtained explicitly for a variety of models, and regularized and renormalized in the momentum representation, which allows for theoretically and computationally feasible implementations of the dual theories. The mapping is rewritten as a gauge interaction, and one-dimensional anyons are also considered.

Related papers

• Particle exchange statistics beyond fermions and bosons [12.031278034659872]
  It is commonly believed that there are only two types of particle exchange statistics in quantum mechanics, fermions and bosons. We show that non parastatistics inequivalent to either fermions or bosons can exist in physical systems.
  arXiv  Detail & Related papers  (2023-08-09T19:51:07Z)
• Formation of robust bound states of interacting microwave photons [148.37607455646454]
  One of the hallmarks of interacting systems is the formation of multi-particle bound states. We develop a high fidelity parameterizable fSim gate that implements the periodic quantum circuit of the spin-1/2 XXZ model. By placing microwave photons in adjacent qubit sites, we study the propagation of these excitations and observe their bound nature for up to 5 photons.
  arXiv  Detail & Related papers  (2022-06-10T17:52:29Z)
• Duality between weak and strong interactions in quantum gases [0.0]
  No exact duality connecting strongly interacting bosons to weakly interacting fermions is known. Our derivation relies on regularizing the only point-like interaction between fermions in 1D. This allows one to apply standard methods of diagrammatic theory to strongly interacting bosons.
  arXiv  Detail & Related papers  (2021-09-17T16:12:28Z)
• Fermionization via cavity-assisted infinite-range interactions [0.0]
  We study a one-dimensional array of bosons with infinite-range interactions mediated by a laser-driven dissipative optical cavity. The cavity-mediated infinite-range interactions open up a new pathway to fermionization, hitherto only known for dipolar bosons.
  arXiv  Detail & Related papers  (2021-07-08T18:00:00Z)
• Field-theoretical aspects of one-dimensional Bose and Fermi gases with contact interactions [0.0]
  We investigate local quantum field theories for 1D Bose and Fermi gases with contact interactions. Because of this three-body coupling, the three-body contact characterizing a local correlation appears in the energy relation for fermions. The triads for the Tonks-Girardeau gas, which is a Bose gas with a hardcore repulsion, as well as the Bose-Fermi correspondence in the presence of three-body attractions are also discussed.
  arXiv  Detail & Related papers  (2020-11-24T09:04:03Z)
• Universal duality transformations in interacting one-dimensional quantum systems [0.2741266294612775]
  I develop a theory of unitary transformations between one-dimensional quantum systems of bosons and fermions with arbitrary spin or internal structure. These transformations generate families of new duality relations and models that relate the strong and weak coupling limits of the respective dual theories.
  arXiv  Detail & Related papers  (2020-09-01T18:00:00Z)
• Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
  We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
  arXiv  Detail & Related papers  (2020-06-03T17:54:43Z)
• 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)
• External and internal wave functions: de Broglie's double-solution theory? [77.34726150561087]
  We propose an interpretative framework for quantum mechanics corresponding to the specifications of Louis de Broglie's double-solution theory. The principle is to decompose the evolution of a quantum system into two wave functions. For Schr"odinger, the particles are extended and the square of the module of the (internal) wave function of an electron corresponds to the density of its charge in space.
  arXiv  Detail & Related papers  (2020-01-13T13:41:24Z)
• Permutation Phase and Gentile Statistics [13.505175620668993]
  It is shown that a finite textitcapacity q -- the maximally allowed particle occupation of each quantum state, naturally arises. The relation between the permutation phase and capacity is given, interpolating between fermions and bosons in the sense of both exchange phase and occupation number.
  arXiv  Detail & Related papers  (2020-01-09T04:16:13Z)

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.