Longitudinal magnetization dynamics in the quantum Ising ring: A Pfaffian method based on correspondence between momentum space and real space

Wu, Ning

doi:10.1103/physreve.101.042108

Cited by 10 publications

(6 citation statements)

References 43 publications

(74 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In passing we mention that a new formalism based on the correspondence between momentum space and real space has been recently put forward in Ref. [70], which would enable to evaluate the longitudinal magnetization for considerably larger system sizes, by numerically computing suitable Pfaffians. Nonetheless, as we shall see in a moment, brute-force diagonalization will be sufficient to infer the main dynamical features we are interested in.…”

Section: Quenches From the Ordered Statementioning

confidence: 99%

Dynamics after quenches in one-dimensional quantum Ising-like systems

Rossini

Vicari

2020

Phys. Rev. B

View full text Add to dashboard Cite

We study the out-of-equilibrium dynamics of one-dimensional quantum Ising-like systems, arising from sudden quenches of the Hamiltonian parameter g driving quantum transitions between disordered and ordered phases. In particular, we consider quenches to values of g around the critical value gc, and mainly address the question whether, and how, the quantum transition leaves traces in the evolution of the transverse and longitudinal magnetizations during such a deep out-of-equilibrium dynamics. We shed light on the emergence of singularities in the thermodynamic infinite-size limit, likely related to the integrability of the model. Finite systems in periodic and open boundary conditions develop peculiar power-law finite-size scaling laws related to revival phenomena, but apparently unrelated to the quantum transition, because their main features are generally observed in quenches to generic values of g. We also investigate the effects of dissipative interactions with an environment, modeled by a Lindblad equation with local decay and pumping dissipation operators within the quadratic fermionic model obtainable by a Jordan-Wigner mapping. Dissipation tends to suppress the main features of the unitary dynamics of closed systems. We finally address the effects of integrability breaking, due to further lattice interactions, such as in anisotropic next-to-nearest neighbor Ising (ANNNI) models. We show that some qualitative features of the post-quench dynamics persist, in particular the different behaviors when quenching to quantum ferromagnetic and paramagnetic phases, and the revival phenomena due to the finite size of the system.

show abstract

Section: Quenches From the Ordered Statementioning

confidence: 99%

Dynamics after quenches in one-dimensional quantum Ising-like systems

Rossini

Vicari

2020

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

“…The treatment of such operators is thus beyond the scope of this paper. The systematic treatment of longitudinal magnetization in zero temperature for Ising model with PBC was conducted in [92], with further extensions including observables involving three fermionic operators in [89]. For other approaches, see for example [93] (open boundary conditions) or [61] (exploiting methods of field theory).…”

Section: Summary 31: Exact Partition Function For Spin-mentioning

confidence: 99%

Exact thermal properties of free-fermionic spin chains

2021

View full text Add to dashboard Cite

An exact description of integrable spin chains at finite temperature is provided using an elementary algebraic approach in the complete Hilbert space of the system. We focus on spin chain models that admit a description in terms of free fermions, including paradigmatic examples such as the one-dimensional transverse-field quantum Ising and XY models. The exact partition function is derived and compared with the ubiquitous approximation in which only the positive parity sector of the energy spectrum is considered. Errors stemming from this approximation are identified in the neighborhood of the critical point at low temperatures. We further provide the full counting statistics of a wide class of observables at thermal equilibrium and characterize in detail the thermal distribution of the kink number and transverse magnetization in the transverse-field quantum Ising chain.

show abstract

“…Dealing with such operators is particularly difficult because subspaces with different momenta mix. For some methods and results involving ground states, see for example [31]. We shall make use of the following propositions: Proposition 1.…”

Section: Structure Of the Hilbert Spacementioning

confidence: 99%

Uhlmann Fidelity and Fidelity Susceptibility for Integrable Spin Chains at Finite Temperature: Exact Results

Białończyk,

Gómez-Ruiz,

del Campo

2021

Preprint

View full text Add to dashboard Cite

We derive the exact expression for the Uhlmann fidelity between arbitrary thermal Gibbs states of the quantum XY model in a transverse field with finite system size. Using it, we conduct a thorough analysis of the fidelity susceptibility of thermal states for the Ising model in a transverse field. We compare the exact results with a common approximation that considers only the positive-parity subspace, which is shown to be valid only at high temperatures. The proper inclusion of the odd parity subspace leads to the enhancement of maximal fidelity susceptibility in the intermediate range of temperatures. We show that this enhancement persists in the thermodynamic limit and scales quadratically with the system size. The correct low-temperature behavior is captured by an approximation involving the two lowest many-body energy eigenstates, from which simple expressions are obtained for the thermal susceptibility and specific heat.

show abstract

Longitudinal magnetization dynamics in the quantum Ising ring: A Pfaffian method based on correspondence between momentum space and real space

Cited by 10 publications

References 43 publications

Dynamics after quenches in one-dimensional quantum Ising-like systems

Dynamics after quenches in one-dimensional quantum Ising-like systems

Exact thermal properties of free-fermionic spin chains

Uhlmann Fidelity and Fidelity Susceptibility for Integrable Spin Chains at Finite Temperature: Exact Results

Contact Info

Product

Resources

About