One-Dimensional Quantum Systems with Ground-State of Jastrow Form Are Integrable

• URL: http://arxiv.org/abs/2201.08282v2
• Date: Sun, 31 Jul 2022 07:40:57 GMT
• Title: One-Dimensional Quantum Systems with Ground-State of Jastrow Form Are Integrable
• Authors: Jing Yang and Adolfo del Campo
• Abstract summary: We establish an equivalence between models described by EOF and the complete family of parent Hamiltonians (PHJ) describing quantum many-body models with ground-states of Jastrow form. Using this construction we establish the integrability of the long-range Lieb-Liniger model, describing bosons in a harmonic trap and subject to contact and Coulomb interactions in one dimension.
• Score: 3.0616044531734192
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The exchange operator formalism (EOF) describes many-body integrable systems using phase-space variables involving an exchange operator that acts on any pair of particles. We establish an equivalence between models described by EOF and the complete infinite family of parent Hamiltonians (PHJ) describing quantum many-body models with ground-states of Jastrow form. This makes it possible to identify the invariants of motion for any model in the PHJ family and establish its integrability, even in the presence of an external potential. Using this construction we establish the integrability of the long-range Lieb-Liniger model, describing bosons in a harmonic trap and subject to contact and Coulomb interactions in one dimension. We give a variety of examples exemplifying the integrability of Hamiltonians in this family.

Related papers

• Integral quantization based on the Heisenberg-Weyl group [39.58317527488534]
  We develop a framework of integral quantization applied to the motion of spinless particles in the four-dimensional Minkowski spacetime. The proposed scheme is based on coherent states generated by the action of the Heisenberg-Weyl group. A direct application of our model, including a computation of transition amplitudes between states characterized by fixed positions and momenta, is postponed to a forthcoming article.
  arXiv  Detail & Related papers  (2024-10-31T14:36:38Z)
• Generalized hydrodynamics of integrable quantum circuits [0.0]
  We study the integrable Trotterization of a prototypical integrable model, the XXZ Heisenberg spin chain. We find that a single microscopic defect at the junction, such as the addition of a single qubit, may change the nonequilibrium macrostate appearing at late time.
  arXiv  Detail & Related papers  (2024-08-01T11:25:26Z)
• Variational quantum simulation using non-Gaussian continuous-variable systems [39.58317527488534]
  We present a continuous-variable variational quantum eigensolver compatible with state-of-the-art photonic technology. The framework we introduce allows us to compare discrete and continuous variable systems without introducing a truncation of the Hilbert space.
  arXiv  Detail & Related papers  (2023-10-24T15:20:07Z)
• Particle-field duality in QFT measurements [0.0]
  Pointlike systems coupled to quantum fields are often employed as toy models for measurements in quantum field theory. We show that in models that work in the strong coupling regime, the apparatus is correlated with smeared field amplitudes, while in models that work in weak coupling the apparatus records particle aspects of the field.
  arXiv  Detail & Related papers  (2023-08-28T17:18:49Z)
• Entanglement dynamics of thermofield double states in integrable models [0.0]
  We study the entanglement dynamics of thermofield double (TFD) states in integrable spin chains and quantum field theories. We show that, for a natural choice of the Hamiltonian eigenbasis, the TFD evolution may be interpreted as a quantum quench from an initial state. We conjecture a formula for the entanglement dynamics, which is valid for both discrete and continuous integrable field theories.
  arXiv  Detail & Related papers  (2021-12-03T16:40:36Z)
• Parent Hamiltonians of Jastrow Wavefunctions [0.0]
  We find the complete family of many-body quantum Hamiltonians with ground-state of Jastrow form. We generalize the Calogero-Marchioro construction for the three-dimensional case to arbitrary spatial dimensions. We show how the pair function can be reverse-engineered to construct models with a given potential.
  arXiv  Detail & Related papers  (2021-07-06T20:03:43Z)
• 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)
• Evolution of a Non-Hermitian Quantum Single-Molecule Junction at Constant Temperature [62.997667081978825]
  We present a theory for describing non-Hermitian quantum systems embedded in constant-temperature environments. We find that the combined action of probability losses and thermal fluctuations assists quantum transport through the molecular junction.
  arXiv  Detail & Related papers  (2021-01-21T14:33:34Z)
• 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)
• Exact ground states of quantum many-body systems under confinement [0.0]
  knowledge of the ground state of a homogeneous quantum many-body system can be used to find the exact ground state of a dual inhomogeneous system with a confining potential. For the complete family of parent Hamiltonians with a ground state of Bijl-Jastrow form in free space, the dual system is shown to include a one-body harmonic potential and two-body long-range interactions.
  arXiv  Detail & Related papers  (2020-05-08T08:39:00Z)
• Multidimensional dark space and its underlying symmetries: towards dissipation-protected qubits [62.997667081978825]
  We show that a controlled interaction with the environment may help to create a state, dubbed as em dark'', which is immune to decoherence. To encode quantum information in the dark states, they need to span a space with a dimensionality larger than one, so different states act as a computational basis. This approach offers new possibilities for storing, protecting and manipulating quantum information in open systems.
  arXiv  Detail & Related papers  (2020-02-01T15:57:37Z)

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.