We study a class of spin- $1/2$ quantum ladder models with generalized plaquette interactions in the presence of a transverse field. We show that in certain parameter regimes, these models have strong zero modes responsible for the long relaxation times of edge spins. By exploiting an infinite set of symmetries in these systems, we show how their Hamiltonians can be represented, in each symmetry sector, by a transverse field Ising chain. Due to the presence of an extensive number of conserved quantities, even if the original system has no disorder, most of these symmetry sectors feature a quasirandom transverse field profile. This representation of the ladder system in terms of a disordered Ising chain allows us to explain the features of the edge autocorrelation function of the original system. Furthermore, we find what appears to be an interesting mechanism for slow decorrelation: Even in parameter regimes where the full ladder model does not possess an obvious strong zero mode, some of the initial information stored in the edge spins can be preserved for long times as a consequence of the existence of strong zero modes within individual symmetry sectors.We study a class of spin-$1/2$ quantum ladder models with generalized plaquette interactions in the presence of a transverse field. We show that in certain parameter regimes, these models have strong zero modes responsible for the long relaxation times of edge spins. By exploiting an infinite set of symmetries in these systems, we show how their Hamiltonians can be represented, in each symmetry sector, by a transverse field Ising chain. Due to the presence of an extensive number of conserved quantities, even if the original system has no disorder, most of these symmetry sectors feature a quasirandom transverse field profile. This representation of the ladder system in terms of a disordered Ising chain allows us to explain the features of the edge autocorrelation function of the original system. Furthermore, we find what appears to be an interesting mechanism for slow decorrelation: Even in parameter regimes where the full ladder model does not possess an obvious strong zero mode, some of the initial information stored in the edge spins can be preserved for long times as a consequence of the existence of strong zero modes within individual symmetry sectors.

arXiv:1901.10211Physical review. B./Physical review. BJul 22, 201927 citations

Local dynamics and thermal activation in the transverse-field Ising chain

Jiahao Yang, Weishi Yuan, Takashi Imai +3 more

There has been considerable recent progress in identifying candidate materials for the transverse-field Ising chain (TFIC), a paradigmatic model for quantum criticality. Here, we study the local spin dynamical structure factor of different spin components in the quantum disordered region of the TFIC. We show that the low-frequency local dynamics of the spins in the Ising- and transverse-field directions have strikingly distinctive temperature dependencies. This leads to the thermal-activation gap for the secular term of the nuclear magnetic resonance $1/{T}_{2}^{\ensuremath{'}}$ relaxation rate to be half of that for the $1/{T}_{1}$ relaxation rate. Our findings reveal a surprise in the nonzero-temperature dynamics of the venerable TFIC model and uncover a means to evince the material realization of the TFIC universality.There has been considerable recent progress in identifying candidate materials for the transverse-field Ising chain (TFIC), a paradigmatic model for quantum criticality. Here, we study the local spin dynamical structure factor of different spin components in the quantum disordered region of the TFIC. We show that the low-frequency local dynamics of the spins in the Ising- and transverse-field directions have strikingly distinctive temperature dependencies. This leads to the thermal-activation gap for the secular term of the nuclear magnetic resonance $1/{T}_{2}^{\ensuremath{'}}$ relaxation rate to be half of that for the $1/{T}_{1}$ relaxation rate. Our findings reveal a surprise in the nonzero-temperature dynamics of the venerable TFIC model and uncover a means to evince the material realization of the TFIC universality.

arXiv:2111.15107Physical review. B./Physical review. BSep 29, 202210 citations

Many-body dynamics of the transverse-field Ising model

Alexander Pikovski, Johannes Schachenmayer, Ana María Rey

Bulletin of the American Physical SocietyJun 5, 20140 citations

Molecular-dynamics study of the classical Ising model in a transverse field

Peter Prelovšek, Igor Sega

The molecular-dynamics technique is applied to the study of the classical ($S=\ensuremath{\infty}$) Ising model in a transverse field on a simple-cubic lattice. The results for the longitudinal- and transverse-relaxation shape function are presented for a set of temperatures in the disordered phase at one value of the transverse field. The longitudinal spectra at $T=\ensuremath{\infty}$ and in the critical regime are analyzed via the Mori's continued-fraction expansion and compared with various approximate results within this approach. The relation of the observed central mode to a domain-wall motion is also discussed. However, due to heavy-damping phenomena no well-defined propagating modes are observed in the critical region. Finally, transverse correlation functions are tested against their diffusive character.The molecular-dynamics technique is applied to the study of the classical ($S=\ensuremath{\infty}$) Ising model in a transverse field on a simple-cubic lattice. The results for the longitudinal- and transverse-relaxation shape function are presented for a set of temperatures in the disordered phase at one value of the transverse field. The longitudinal spectra at $T=\ensuremath{\infty}$ and in the critical regime are analyzed via the Mori's continued-fraction expansion and compared with various approximate results within this approach. The relation of the observed central mode to a domain-wall motion is also discussed. However, due to heavy-damping phenomena no well-defined propagating modes are observed in the critical region. Finally, transverse correlation functions are tested against their diffusive character.

Physical review. B, Condensed matterJun 1, 19789 citations

We study a class of spin-

1/2

quantum ladder models with generalized plaquette interactions in the presence of a transverse field. We show that in certain parameter regimes, these models have strong zero modes responsible for the long relaxation times of edge spins. By exploiting an infinite set of symmetries in these systems, we show how their Hamiltonians can be represented, in each symmetry sector, by a transverse field Ising chain. Due to the presence of an extensive number of conserved quantities, even if the original system has no disorder, most of these symmetry sectors feature a quasirandom transverse field profile. This representation of the ladder system in terms of a disordered Ising chain allows us to explain the features of the edge autocorrelation function of the original system. Furthermore, we find what appears to be an interesting mechanism for slow decorrelation: Even in parameter regimes where the full ladder model does not possess an obvious strong zero mode, some of the initial information stored in the edge spins can be preserved for long times as a consequence of the existence of strong zero modes within individual symmetry sectors.

1/{T}_{1}

relaxation rate. Our findings reveal a surprise in the nonzero-temperature dynamics of the venerable TFIC model and uncover a means to evince the material realization of the TFIC universality.