Generalization of group-theoretic coherent states for variational calculations

@article{Guaita2021GeneralizationOG,
  title={Generalization of group-theoretic coherent states for variational calculations},
  author={T. Guaita and Lucas Hackl and Tao Shi and Eugene A. Demler and Juan Ignacio Cirac},
  journal={Physical Review Research},
  year={2021},
  volume={3}
}
The authors introduce a class of quantum states for variational studies that exhibits entanglement while still admitting efficient computation of expectation values. 

Figures from this paper

Quasienergy operators and generalized squeezed states for systems of trapped ions

Variational Ansatz for the Ground State of the Quantum Sherrington-Kirkpatrick Model

We present an ansatz for the ground states of the Quantum Sherrington-Kirkpatrick model, a paradigmatic model for quantum spin glasses. Our ansatz, based on the concept of generalized coherent

Algorithm for initializing a generalized fermionic Gaussian state on a quantum computer

We present explicit expressions for the central piece of a variational method developed by Shi et al (2018 Ann. Phys. 390 245) which extends variational wave functions that are efficiently computable

Bosonic and fermionic Gaussian states from Kähler structures

We show that bosonic and fermionic Gaussian states (also known as ``squeezed coherent states’’) can be uniquely characterized by their linear complex structure JJ which is a linear map on the

References

SHOWING 1-10 OF 36 REFERENCES

Coherent states for arbitrary Lie group

The concept of coherent states originally closely related to the nilpotent group of Weyl is generalized to arbitrary Lie group. For the simplest Lie groups the system of coherent states is

Coherent states: Theory and some Applications

In this review, a general algorithm for constructing coherent states of dynamical groups for a given quantum physical system is presented. The result is that, for a given dynamical group, the

Geometry of variational methods: dynamics of closed quantum systems

We present a systematic geometric framework to study closed quantum systems based on suitably chosen variational families. For the purpose of (A) real time evolution, (B) excitation spectra, (C)

Algebraic approach to interacting quantum systems

An algebraic framework for interacting extended quantum systems to study complex phenomena characterized by the coexistence and competition of different states of matter is presented and the novel concept of emergent symmetry is introduced as another symmetry guiding principle.

Symplectic Geometry and Quantum Mechanics

Symplectic Geometry.- Symplectic Spaces and Lagrangian Planes.- The Symplectic Group.- Multi-Oriented Symplectic Geometry.- Intersection Indices in Lag(n) and Sp(n).- Heisenberg Group, Weyl Calculus,

Local optimization on pure Gaussian state manifolds

An efficient local optimization algorithm to extremize arbitrary functions on these families of Gaussian states based on notions of gradient descent attuned to the local geometry and the natural group action of the symplectic and orthogonal group is exploited.

Quantum-to-classical correspondence and hubbard-stratonovich dynamical systems: A lie-algebraic approach

We propose a Lie-algebraic duality approach to analyze nonequilibrium evolution of closed dynamical systems and thermodynamics of interacting quantum lattice models (formulated in terms of

SU(N) coherent states

We generalize Schwinger boson representation of SU(2) algebra to SU(N) and define coherent states of SU(N) using 2(2N−1−1) bosonic harmonic oscillator creation and annihilation operators. We give an