Universal duality transformations in interacting one-dimensional quantum systems

• URL: http://arxiv.org/abs/2009.00614v2
• Date: Sat, 17 Oct 2020 07:00:48 GMT
• Title: Universal duality transformations in interacting one-dimensional quantum systems
• Authors: Manuel Valiente
• Abstract summary: 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.
• Score: 0.2741266294612775
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: One-dimensional quantum systems admit duality relations that put hard core spinless bosons and fermions in one-to-one correspondence via Girardeau's mapping theorem. The simplest models of soft bosons interacting via zero-range potentials can also be mapped onto dual interacting fermions. However, a systematic approach to one-dimensional statistical transmutation for arbitrary low-energy interactions in the spinless and spinful or multicomponent cases has remained elusive. I develop a general theory of local unitary transformations between one-dimensional quantum systems of bosons and fermions with arbitrary spin or internal structure, single-particle dispersion -- including non-relativistic, relativistic or otherwise -- and low-energy interactions in the universal regime. These transformations generate families of new duality relations and models that relate the strong and weak coupling limits of the respective dual theories.

Related papers

• Theory of the correlated quantum Zeno effect in a monitored qubit dimer [41.94295877935867]
  We show how the competition between two measurement processes give rise to two distinct Quantum Zeno (QZ) regimes. We develop a theory based on a Gutzwiller ansatz for the wavefunction that is able to capture the structure of the Hilbert phase diagram. We show how the two QZ regimes are intimately connected to the topology of the flow of the underlying non-Hermitian Hamiltonian governing the no-click evolution.
  arXiv  Detail & Related papers  (2025-03-28T19:44:48Z)
• Harnessing Chiral Spin States in Molecular Nanomagnets for Quantum Technologies [44.1973928137492]
  We show that chiral qubits naturally suppress always-on interactions that can not be switched off in weakly coupled qubits. Our findings establish spin chirality engineering as a promising strategy for mitigating always-on interaction in entangling two chiral qubits in molecular quantum technologies.
  arXiv  Detail & Related papers  (2025-01-21T08:23:12Z)
• A minimal tensor network beyond free fermions [39.847063110051245]
  This work proposes a minimal model extending the duality between classical statistical spin systems and fermionic systems. A Jordan-Wigner transformation applied to a two-dimensional tensor network maps the partition sum of a classical statistical mechanics model to a Grassmann variable integral. The resulting model is simple, featuring only two parameters: one governing spin-spin interaction and the other measuring the deviation from the free fermion limit.
  arXiv  Detail & Related papers  (2024-12-05T14:49:39Z)
• Emergent Anomalous Hydrodynamics at Infinite Temperature in a Long-Range XXZ Model [14.297989605089663]
  We find anomalous hydrodynamics in a spin-1/2 XXZ chain with power-law couplings. We quantify the degree of quantum chaos using the Kullback-Leibler divergence. This work offers another deep understanding of emergent anomalous transport phenomena in a wider range of non-integrable quantum many-body systems.
  arXiv  Detail & Related papers  (2024-03-26T17:50:04Z)
• 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)
• Dispersive Non-reciprocity between a Qubit and a Cavity [24.911532779175175]
  We present an experimental study of a non-reciprocal dispersive-type interaction between a transmon qubit and a superconducting cavity. We show that the qubit-cavity dynamics is well-described in a wide parameter regime by a simple non-reciprocal master-equation model.
  arXiv  Detail & Related papers  (2023-07-07T17:19:18Z)
• The Composite Particle Duality: A New Class of Topological Quantum Matter [0.0]
  Composite particle duality extends notions of flux attachment and statistical transmutation in spacetime dimensions beyond 2+1D. The immediate implication of the duality is that an interacting quantum system in arbitrary dimensions can experience a modification of its statistical properties if coupled to a certain gauge field.
  arXiv  Detail & Related papers  (2023-06-01T15:46:49Z)
• Interaction-induced topological pumping in a solid-state quantum system [18.7657779101508]
  Inter-particle interaction can profoundly alter the band structure of quantum many-body systems. Here we demonstrate interaction-induced topological pumping in a solid-state quantum system comprising an array of 36 superconducting qubits.
  arXiv  Detail & Related papers  (2023-03-08T13:57:13Z)
• 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)
• Electric circuit emulation of topological transitions driven by quantum statistics [0.0]
  We predict the topological transition in the two-particle interacting system driven by the particles' quantum statistics. As a toy model, we investigate an extended one-dimensional Hubbard model with two anyonic excitations obeying fractional quantum statistics. We develop a rigorous method to emulate the eigenmodes and eigenenergies of anyon pairs with resonant electric circuits.
  arXiv  Detail & Related papers  (2021-08-23T22:34:52Z)
• Transition-state dynamics in complex quantum systems [0.0]
  We study the reaction dynamics in complex quantum systems in which the complete mixing of states is hindered by an internal barrier. The validity of the transition-state theory is questionable when there is no identifiable coordinate associated with the barrier. We find that the transition-state formula can be derived from the model under some easily justifiable approximations.
  arXiv  Detail & Related papers  (2021-05-25T16:51:30Z)
• Quantum liquids and droplets with low-energy interactions in one dimension [0.20646127669654826]
  We study the role of effective three-body repulsion, in systems with weak attractive pairwise interactions. At zero temperature, the equations of state in both theories agree quantitatively at low densities for overall repulsion. We develop analytical tools to investigate the properties of the theory, and obtain astounding agreement with exact numerical calculations.
  arXiv  Detail & Related papers  (2021-03-30T16:56:01Z)
• Molecular Interactions Induced by a Static Electric Field in Quantum Mechanics and Quantum Electrodynamics [68.98428372162448]
  We study the interaction between two neutral atoms or molecules subject to a uniform static electric field. Our focus is to understand the interplay between leading contributions to field-induced electrostatics/polarization and dispersion interactions.
  arXiv  Detail & Related papers  (2021-03-30T14:45:30Z)
• Bose-Fermi dualities for arbitrary one-dimensional quantum systems in the universal low energy regime [0.2741266294612775]
  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.
  arXiv  Detail & Related papers  (2020-09-01T18:00:04Z)
• A non-relativistic theory of quantum mechanics and gravity with local modulus symmetry [5.194627108018866]
  Inspired by the similarities between quantum field theory and general relativity, we set out to construct a non-relativistic theory of quantum mechanics and gravity. Three quantum metric functions are defined to signify the kinematic change of quantum state brought by gravity. New features in these equations offer potential mechanisms to account for the dark energy, the mass discrepancies in the universe, and the quantum state reduction of macroscopic objects.
  arXiv  Detail & Related papers  (2020-08-18T05:36:11Z)

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.