Liouville coherent states

Ringel, Matouš; Gritsev, Vladimir

doi:10.1209/0295-5075/99/20012

Cited by 6 publications

(4 citation statements)

References 15 publications

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“…We call the procedure of going from the time-ordered exponential to the product of the ordinary exponentials a disentanglement transformation. Similar philosophy has been recently used in [10][11][12][13][14][15][16][17][18][19][20].…”

Section: Disentanglement Of the Time-ordered Exponentialmentioning

confidence: 99%

Dynamical symmetry approach to path integrals of quantum spin systems

2013

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We develop a dynamical symmetry approach to path integrals for general interacting quantum spin systems. The time-ordered exponential obtained after the Hubbard-Stratonovich transformation can be disentangled into the product of a finite number of the usual exponentials. This procedure leads to a set of stochastic differential equations on the group manifold, which can be further formulated in terms of the supersymmetric effective action. This action has the form of the Witten topological field theory in the continuum limit. As a consequence, we show how it can be used to obtain the exact results for a specific quantum many-body system which can be otherwise solved only by the Bethe ansatz. This represents an example of a many-body system treated exactly using the path-integral formulation. Moreover, our method can deal with time-dependent parameters, which we demonstrate explicitly.

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Section: Disentanglement Of the Time-ordered Exponentialmentioning

confidence: 99%

Dynamical symmetry approach to path integrals of quantum spin systems

2013

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“…In addition to the results presented above, disentangling (38) allows studying the dynamics of the open system in a basis of coherent states in Liouville space. This has been done recently for one two-level system interacting with a bosonic bath [46]. Working in the Heisenberg picture, the same procedure allows finding conserved quantities of the open system [47].…”

Section: < mentioning

confidence: 99%

Algebraic solution of the Lindblad equation for a collection of multilevel systems coupled to independent environments

Bolaños¹,

Barberis-Blostein²

2015

J. Phys. A: Math. Theor.

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We consider the Lindblad equation for a collection of multilevel systems coupled to independent environments. The equation is symmetric under the exchange of the labels associated with each system and thus the open-system dynamics takes place in the permutation-symmetric subspace of the operator space. The dimension of this space grows polynomially with the number of systems. We construct a basis of this space and a set of superoperators whose action on this basis is easily specified. For a given number of levels, M , these superoperators are written in terms of a bosonic realization of the generators of the Lie algebra sl(M 2 ). In some cases, these results enable finding an analytic solution of the master equation using known Lie-algebraic methods. To demonstrate this, we obtain an analytic expression for the state operator of a collection of threelevel atoms coupled to independent radiation baths. When analytic solutions are difficult to find, the basis and the superoperators can be used to considerably reduce the computational resources required for simulations.

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“…Exact solutions have been given for quadratic fermionic systems [2][3][4][5][6], but this excludes most bulk dissipation in spin systems. Various algebraic methods have been used to solve Lindblad equations [7][8][9], requiring the unitary and dissipative parts to form a closed algebra. Finally, very specific models have been mapped to integrable closed systems, solvable by Bethe ansatz [10].…”

Section: Introductionmentioning

confidence: 99%

Symmetry-protected coherent relaxation of open quantum systems

Caspel

Gritsev

2018

Phys. Rev. A

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We compute the effect of Markovian bulk dephasing noise on the staggered magnetization of the spin-1 2 XXZ Heisenberg chain, as the system evolves after a Néel quench. For sufficiently weak system-bath coupling, the unitary dynamics are found to be preserved up to a single exponential damping factor. This is a consequence of the interplay between PT symmetry and weak symmetries, which strengthens previous predictions for PT-symmetric Liouvillian dynamics. Requirements are a non-degenerate PT-symmetric generator of time evolutionL, a weak parity symmetry and an observable that is anti-symmetric under this parity transformation. The spectrum ofL then splits up into symmetry sectors, yielding the same decay rate for all modes that contribute to the observable's time evolution. This phenomenon may be realized in trapped ion experiments and has possible implications for the control of decoherence in out-of-equilibrium many-body systems.

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Liouville coherent states

Cited by 6 publications

References 15 publications

Dynamical symmetry approach to path integrals of quantum spin systems

Dynamical symmetry approach to path integrals of quantum spin systems

Algebraic solution of the Lindblad equation for a collection of multilevel systems coupled to independent environments

Symmetry-protected coherent relaxation of open quantum systems

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