When matter in different phases is brought into contact, an interface with unexpected properties can emerge. In the transverse-field Ising chain, the authors investigate the interface formed by joining a disordered state with a ferromagnetically ordered one. They show that, within this emergent region, order parameters and entanglement asymmetries of subsystems exhibit universal behavior. Correlations extend across the entire region, and the Wigner--Yanase skew information of large subsystems reveals macroscopic multipartite entanglement.When matter in different phases is brought into contact, an interface with unexpected properties can emerge. In the transverse-field Ising chain, the authors investigate the interface formed by joining a disordered state with a ferromagnetically ordered one. They show that, within this emergent region, order parameters and entanglement asymmetries of subsystems exhibit universal behavior. Correlations extend across the entire region, and the Wigner--Yanase skew information of large subsystems reveals macroscopic multipartite entanglement.

arXiv:2411.04089Physical review. B./Physical review. BMay 14, 20256 citations

Dynamics of disordered Ising model in the transverse field

Peter Prelovšek

Jan 1, 19760 citations

Finite-size scaling analysis of the two-dimensional random transverse-field Ising ferromagnet

Jiwon Choi, Seung Ki Baek

The random transverse-field Ising ferromagnet (RTFIF) is a highly disordered quantum system which contains randomness in the coupling strengths as well as in the transverse-field strengths. In one dimension, the critical properties are governed by an infinite-randomness fixed point (IRFP), and renormalization-group studies argue that the two-dimensional (2D) model is also governed by an IRFP. However, even the location of the critical point remains unsettled among quantum Monte Carlo (QMC) studies. In this work, we perform extensive QMC simulations to locate the quantum critical point and attempt a finite-size scaling analysis to observe the critical behavior. We estimate the critical field strength of the 2D RTFIF as ${\mathrm{\ensuremath{\Gamma}}}_{c}=7.52(2)$, together with critical exponents such as $\ensuremath{\beta}=1.5(3), \ensuremath{\nu}=1.6(3)$, and $z=3.3(3)$ or $\ensuremath{\psi}=0.50(3)$. We have also considered the McCoy-Wu model, which has randomness in the ferromagnetic coupling strengths but not in the transverse-field strength. Our QMC calculation shows that the critical behavior of the 2D McCoy-Wu model is closer to that of the 2D transverse-field Ising spin glass than to that of the 2D RTFIF. These numerical findings enhance our understanding of disordered 2D quantum systems.The random transverse-field Ising ferromagnet (RTFIF) is a highly disordered quantum system which contains randomness in the coupling strengths as well as in the transverse-field strengths. In one dimension, the critical properties are governed by an infinite-randomness fixed point (IRFP), and renormalization-group studies argue that the two-dimensional (2D) model is also governed by an IRFP. However, even the location of the critical point remains unsettled among quantum Monte Carlo (QMC) studies. In this work, we perform extensive QMC simulations to locate the quantum critical point and attempt a finite-size scaling analysis to observe the critical behavior. We estimate the critical field strength of the 2D RTFIF as ${\mathrm{\ensuremath{\Gamma}}}_{c}=7.52(2)$, together with critical exponents such as $\ensuremath{\beta}=1.5(3), \ensuremath{\nu}=1.6(3)$, and $z=3.3(3)$ or $\ensuremath{\psi}=0.50(3)$. We have also considered the McCoy-Wu model, which has randomness in the ferromagnetic coupling strengths but not in the transverse-field strength. Our QMC calculation shows that the critical behavior of the 2D McCoy-Wu model is closer to that of the 2D transverse-field Ising spin glass than to that of the 2D RTFIF. These numerical findings enhance our understanding of disordered 2D quantum systems.

arXiv:2310.14756Physical review. B./Physical review. BOct 20, 20233 citations

Dynamic critical behavior of random spin chains in a field

Iveta R. Pimentel, Robin B. Stinchcombe

The dynamic critical behavior of one-dimensional random spin systems in a field at zero temperature is investigated by a generalized transfer-matrix scaling technique. Three spin models are considered: Heisenberg in a longitudinal field, XY in a transverse field, and Ising in a transverse field, with either spin-glass or random-field disorder. Near the transition, i.e., for small values of the reduced field \ensuremath{\Delta}=(H- ${H}_{c}$ ), where ${H}_{c}$ is the critical field, one finds that the dispersion relation for the low-frequency \ensuremath{\omega}, small-wave-vector k spin-wave excitations takes the scaling form \ensuremath{\omega}= ${k}^{z}$ f(\ensuremath{\Delta}/ ${k}^{\mathrm{cphi}}$ ), and exact results are given for the dynamic exponent z and crossover exponent cphi. This form contains a crossover of the frequency \ensuremath{\omega} between two different asymptotic behaviors: ${k}^{z}$ for \ensuremath{\Delta}\ensuremath{\ll} ${k}^{\mathrm{cphi}}$ and ${h}^{\ensuremath{\delta}}$ for \ensuremath{\Delta}\ensuremath{\gg} ${k}^{\mathrm{cphi}}$ , where the field exponent is \ensuremath{\delta}=z/cphi. In the case of the Heisenberg systems the spin-glass disorder gives rise to the nontrivial dynamic exponent z=(3/2, whereas in the random-field case it is the exponent associated to the field that becomes nontrivial, taking the value (4/3. For the transverse XY systems the random-field disorder implies nontrivial values for both the dynamic and field exponents, (3/2 and (3/4, respectively, whereas the spin-glass disorder does not affect the dynamics of the system, which behaves like a pure transverse XY ferromagnet. Finally, for the transverse Ising systems neither the random field nor the spin-glass disorder affects the dynamics, which is the same as for a pure transverse Ising ferromagnet.The dynamic critical behavior of one-dimensional random spin systems in a field at zero temperature is investigated by a generalized transfer-matrix scaling technique. Three spin models are considered: Heisenberg in a longitudinal field, XY in a transverse field, and Ising in a transverse field, with either spin-glass or random-field disorder. Near the transition, i.e., for small values of the reduced field \ensuremath{\Delta}=(H-${H}_{c}$), where ${H}_{c}$ is the critical field, one finds that the dispersion relation for the low-frequency \ensuremath{\omega}, small-wave-vector k spin-wave excitations takes the scaling form \ensuremath{\omega}=${k}^{z}$f(\ensuremath{\Delta}/${k}^{\mathrm{cphi}}$), and exact results are given for the dynamic exponent z and crossover exponent cphi. This form contains a crossover of the frequency \ensuremath{\omega} between two different asymptotic behaviors: ${k}^{z}$ for \ensuremath{\Delta}\ensuremath{\ll}${k}^{\mathrm{cphi}}$ and ${h}^{\ensuremath{\delta}}$ for \ensuremath{\Delta}\ensuremath{\gg}${k}^{\mathrm{cphi}}$, where the field exponent is \ensuremath{\delta}=z/cphi. In the case of the Heisenberg systems the spin-glass disorder gives rise to the nontrivial dynamic exponent z=(3/2, whereas in the random-field case it is the exponent associated to the field that becomes nontrivial, taking the value (4/3. For the transverse XY systems the random-field disorder implies nontrivial values for both the dynamic and field exponents, (3/2 and (3/4, respectively, whereas the spin-glass disorder does not affect the dynamics of the system, which behaves like a pure transverse XY ferromagnet. Finally, for the transverse Ising systems neither the random field nor the spin-glass disorder affects the dynamics, which is the same as for a pure transverse Ising ferromagnet.

Physical review. B, Condensed matterSep 1, 19899 citations

Phase transitions of ferromagnetic Ising films in a transverse field

Enaldo F. Sarmento, J.W. Tucker

Journal of Magnetism and Magnetic MaterialsAug 1, 19930 citations

z=3.3(3)

or $\ensuremath{\psi}=0.50(3)$. We have also considered the McCoy-Wu model, which has randomness in the ferromagnetic coupling strengths but not in the transverse-field strength. Our QMC calculation shows that the critical behavior of the 2D McCoy-Wu model is closer to that of the 2D transverse-field Ising spin glass than to that of the 2D RTFIF. These numerical findings enhance our understanding of disordered 2D quantum systems.

{H}_{c}

), where

{H}_{c}

is the critical field, one finds that the dispersion relation for the low-frequency \ensuremath{\omega}, small-wave-vector k spin-wave excitations takes the scaling form \ensuremath{\omega}=

{k}^{z}

f(\ensuremath{\Delta}/

{k}^{\mathrm{cphi}}

), and exact results are given for the dynamic exponent z and crossover exponent cphi. This form contains a crossover of the frequency \ensuremath{\omega} between two different asymptotic behaviors:

{k}^{z}

for \ensuremath{\Delta}\ensuremath{\ll}

{k}^{\mathrm{cphi}}

and ${h}^{\ensuremath{\delta}}$ for \ensuremath{\Delta}\ensuremath{\gg}

{k}^{\mathrm{cphi}}

, where the field exponent is \ensuremath{\delta}=z/cphi. In the case of the Heisenberg systems the spin-glass disorder gives rise to the nontrivial dynamic exponent z=(3/2, whereas in the random-field case it is the exponent associated to the field that becomes nontrivial, taking the value (4/3. For the transverse XY systems the random-field disorder implies nontrivial values for both the dynamic and field exponents, (3/2 and (3/4, respectively, whereas the spin-glass disorder does not affect the dynamics of the system, which behaves like a pure transverse XY ferromagnet. Finally, for the transverse Ising systems neither the random field nor the spin-glass disorder affects the dynamics, which is the same as for a pure transverse Ising ferromagnet.