Complexity in the Lipkin-Meshkov-Glick model

Pal, Kunal; Pal, Kuntal; Sarkar, Tapobrata

doi:10.1103/physreve.107.044130

Cited by 7 publications

(4 citation statements)

References 59 publications

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“…Starting with the works of [16,74], where the NC was used to probe topological phase transitions, quite a number of studies have appeared along these lines, see e.g. [19][20][21][22][23][24]. However, exploring the zero-temperature QPTs using the recently proposed notion of SC has one significant advantage in that this measure of complexity does not depend on the choice of cost-functional-an essential feature (as well as a drawback in many cases) of Nielsen-type complexities.…”

Section: Discussionmentioning

confidence: 99%

“…Despite the fact that due to the long-range nature of the interaction, it cannot be mapped to free fermion models, in the thermodynamic limit the phases of this model can be worked out, and have been studied extensively in the literature [62,63]. Besides these works on the static properties of the LMG model, the time-dependent fidelity in a quench scenario was studied in [64], and the Nielsen and FSC in [24,65]-where all of these quantities have been shown to have some particular behavior as the system moves toward the critical point.…”

Section: J Stat Mech (2023) 103101mentioning

confidence: 99%

“…The behaviors of CC were explored for the Bose-Hubbard model in [22,23] and for the infinite-range Lipkin-Meshkov-Glick (LMG) model in [24]. On the other hand, the time evolution of CC under a quantum quench and its comparison with entanglement measures of a system can reveal a great deal of information about the underlying dynamics, depending on the integrability property of the Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

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Time evolution of spread complexity in quenched Lipkin–Meshkov–Glick model

Afrasiar,

Basak,

Dey

et al. 2023

J. Stat. Mech.

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We use the spread complexity (SC) of a time-evolved state after a sudden quantum quench in the Lipkin–Meshkov–Glick (LMG) model prepared in the ground state as a probe of the quantum phase transition when the system is quenched toward the critical point. By studying the growth of the effective number of elements of the Krylov basis that contributes to the SC more than a preassigned cutoff, we show how the two phases of the LMG model can be distinguished. We also explore the time evolution of spread entropy after both non-critical and critical quenches. We show that the sum contributing to the spread entropy converges slowly in the symmetric phase of the LMG model compared to that in the broken phase, and for a critical quench, the spread entropy diverges logarithmically at late times.

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Section: Discussionmentioning

confidence: 99%

Section: J Stat Mech (2023) 103101mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Time evolution of spread complexity in quenched Lipkin–Meshkov–Glick model

Afrasiar,

Basak,

Dey

et al. 2023

J. Stat. Mech.

Self Cite

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“…We are not the first to calculate C in a quantum phase transition (QPT) [16]. Recent papers discuss exactly solvable models as the topological Kitaev, Bose-Hubbard Lipkin-Meshkov-Glick ones and conformal field theories [17][18][19][20][21][22][22][23][24][25]. Importantly enough, complexity has been shown to be a useful probe of topological phase transitions.…”

Section: Introductionmentioning

confidence: 99%

Circuit Complexity through phase transitions: Consequences in quantum state preparation

Roca-Jerat,

Sancho-Lorente,

Román-Roche

et al. 2023

SciPost Phys.

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In this paper, we analyze the circuit complexity for preparing ground states of quantum many-body systems. In particular, how this complexity grows as the ground state approaches a quantum phase transition. We discuss different definitions of complexity, namely the one following the Fubini-Study metric or the Nielsen complexity. We also explore different models: Ising, ZZXZ or Dicke. In addition, different forms of state preparation are investigated: analytic or exact diagonalization techniques, adiabatic algorithms (with and without shortcuts), and Quantum Variational Eigensolvers. We find that the divergence (or lack thereof) of the complexity near a phase transition depends on the non-local character of the operations used to reach the ground state. For Fubini-Study based complexity, we extract the universal properties and their critical exponents. In practical algorithms, we find that the complexity depends crucially on whether or not the system passes close to a quantum critical point when preparing the state. For both VQE and Adiabatic algorithms, we provide explicit expressions and bound the growth of complexity with respect to the system size and the execution time, respectively.

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Time evolution of spread complexity and statistics of work done in quantum quenches

Pal,

Gill

et al. 2023

Phys. Rev. B

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Complexity in the Lipkin-Meshkov-Glick model

Cited by 7 publications

References 59 publications

Time evolution of spread complexity in quenched Lipkin–Meshkov–Glick model

Time evolution of spread complexity in quenched Lipkin–Meshkov–Glick model

Circuit Complexity through phase transitions: Consequences in quantum state preparation

Time evolution of spread complexity and statistics of work done in quantum quenches

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