Exact variational dynamics of the multimode Bose-Hubbard model based on 
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 coherent states

Qiao, Yulong; Großmann, Frank

doi:10.1103/physreva.103.042209

Cited by 8 publications

(11 citation statements)

References 45 publications

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“…More insights into the features of the model can be gained from its semiclassical counterpart, which is given by the expectation value of H in equation (1) with respect to the coherent state in the limit N → ∞. The coherent states are defined as [68,81,[88][89][90]…”

Section: Semiclassical Limitmentioning

confidence: 99%

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Understanding dynamical phase transitions in a spinor Bose–Einstein condensate via quantum and semiclassical analyses

Niu,

Wang

2024

Phys. Scr.

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Phase transitions in nonequilibrium dynamics of many body quantum systems, known as dynamical phase transitions (DPTs), play an important role for understandingvarious dynamical phenomena observed in different branches of physics.In general, there are two types of DPTs, the first one is characterized by distinct evolutionary behaviors of a physical observable, while the second one is marked by the vanishing overlap between the time-evolved and initial states. Here, we focus on exploring such DPTs from both quantum and semiclassical perspectives in a spinor Bose-Einstein condensate (BEC), an ideal platform forinvestigating nonequilibrium dynamics.Utilizing the sudden quench process, we demonstrate that the system exhibits both types of DPTs as the control parameter is quenched throughthe critical value, referring to as the critical quenching. We show analytically how to determine the critical quenching viathe semiclassical approach and carry out a detailed examination of both semiclassical and quantum signatures of DPTs. In particular, we reveal that the occurrence of DPTs is triggered bythe separatrix in the underlying semiclassical system.Our findings offer deeper insights into the properties of DPTs and verify the usefulness of semiclassical analysis for studying DPTs in quantum systems with well-defined semiclassical limit. 

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Section: Semiclassical Limitmentioning

confidence: 99%

“…where |N, N 0 〉 are the Fock states and j = f 0 − (f 1 + f −1 )/2 is the relative phase. By using the relation [81,90], one can easily find that the semiclassical limit of H (1) is given by [81,88] a a…”

Section: Semiclassical Limitmentioning

confidence: 99%

Understanding dynamical phase transitions in a spinor Bose–Einstein condensate via quantum and semiclassical analyses

Niu,

Wang

2024

Phys. Scr.

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“…More insights into the properties of the system and associated phase transitions can be gained from the semiclassical analysis in the limit N → ∞. To this end, we calculate the semiclassical counterpart of the Hamiltonian (1) by using the coherent states, defined as [58,71,[77][78][79]…”

Section: Semiclassical Limitmentioning

confidence: 99%

“…( 1) with respect to the coherent state in the classical limit N → ∞. By employing the relation α|a † m a m ′ |α = N α * m α m ′ [71,79], one can easily find that the classical Hamiltonian with N 1 = N −1 (n −1 = n 1 ) reads [71,77]…”

Section: Semiclassical Limitmentioning

confidence: 99%

Excited-state quantum phase transitions and Loschmidt-echo spectra in a spinor Bose-Einstein condensate

Niu

Wang

2023

Phys. Rev. A

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Phase transitions in nonequilibrium dynamics of many body quantum systems, the so-called dynamical phases transition (DPTs), play an important role for understanding various dynamical phenomena observed in different branches of physics. In general, there have two types of DPTs, the first one refers to the phase transition that is characterized by distinct evolution behaviors of a physical observable, while the second one is marked by the nonanalyticities in the rate function of the initial state survival probability. Here, we focus on such DPTs from both quantum and semiclassical perspectives in a spinor Bose-Einstein condensate (BEC), an ideal platform to investigate nonequilibrium dynamics. By using the sudden quench process, we demonstrate that the system exhibits both types of DPTs present as the control parameter quenches through the critical one, referring to as the critical quench. We show analytically how to determine the critical quenches by means of the semiclassical approach and carry out a detailed examination on both semiclassical and quantum signatures of two types of DPTs. Moreover, we further reveal that the occurrence of DPTs is closely connected to the separatrix in the underlying classical system. Our findings provide more insights into the properties of DPTs and verify the usefulness of semiclassical analysis for understanding DPTs in quantum systems with well-defined semiclassical limit.

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“…ZSs can be viewed as Fermionic Coherent States (CS) of a two-level system. Previously Coherent States of the harmonic oscillator have been used to describe Bosonic systems in second quantisation with the help of Herman-Kluck 17 and Coupled Coherent States propagation methods 18 and also with Generalised Coherent States 19 . Second quantisation Hamiltonians look like those of coupled oscillators with the difference that the oscillators represent the amplitudes and populations of the orbitals occupied by Bosons.…”

Section: Introductionmentioning

confidence: 99%

Electronic energies from coupled fermionic 'Zombie' states imaginary time evolution

Bramley,

Hele,

Shalashilin

2022

Preprint

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Zombie States are a recently introduced formalism to describe coupled coherent Fermionic states which address the Fermionic sign problem in a computationally tractable manner.Previously it has been shown that Zombie States with fractional occupations of spin-orbitals obeyed the correct Fermionic creation and annihilation algebra and presented results for real-time evolution 1 . In this work we extend and build on this formalism by developing efficient algorithms for evaluating the Hamiltonian and other operators between Zombie States and address their normalization. We also show how imaginary time propagation can be used to find the ground state of a system. We also present a biasing method, for setting up a basis set of random Zombie States, that allow much smaller basis sizes to be used while still accurately describing the electronic structure Hamiltonian and its ground state and describe a technique of wave function "cleaning" which removes the contributions of configurations with the wrong number of electrons, improving the accuracy further. We also show how low-lying excited states can be calculated efficiently using a Gram-Schmidt orthogonalization procedure.The proposed algorithm of imaginary time propagation on a biased random grids of Zombie States may present an alternative to existing Quantum Monte Carlo methods.

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Exact variational dynamics of the multimode Bose-Hubbard model based on SU(M) coherent states

Cited by 8 publications

References 45 publications

Understanding dynamical phase transitions in a spinor Bose–Einstein condensate via quantum and semiclassical analyses

Understanding dynamical phase transitions in a spinor Bose–Einstein condensate via quantum and semiclassical analyses

Excited-state quantum phase transitions and Loschmidt-echo spectra in a spinor Bose-Einstein condensate

Electronic energies from coupled fermionic 'Zombie' states imaginary time evolution

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