Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physica A Statistical Mechanics and its Applications

Quantum criticality and correlations in the Ising-Gamma chain

Zi-An Liu, Yuli Dong, Ning Wu, Yimin Wang, Wen‐Long You

Published May 28, 2021• 16 citations
Publisher
DOI
10.1016/j.physa.2021.126122

Related papers

Spin correlations in the Ising chains

Baohua Teng, H.K. Sy

Solid State Communications•Feb 12, 2004•6 citations

Vector chiral order and dynamical quantum phase transitions in an Ising chain with dimerized anisotropic Gamma interaction

Yu-Hong Yan, Shi-Qiao Wu, Kun-Liang Zhang

We investigate a transverse-field Ising chain with dimerized anisotropic Gamma interactions and demonstrate that, both in the absence and presence of Ising interactions, the competition between Gamma anisotropy and the transverse field gives rise to vector chiral order and dynamical quantum phase transitions. The phase diagram comprises positive and negative vector chiral phases and a paramagnetic phase, characterized by the vector spin chirality and the vector chiral order parameter. In the absence of Ising interactions, we identify a gapless critical line that exhibits no finite-size drift, along which the spin-spin correlations and subsystem entanglement entropy display behavior distinct from that of Ising criticality. Furthermore, we find that the critical times of dynamical quantum phase transitions form periodic or aperiodic sequences, depending on the quench path. Our findings highlight how dimerized off-diagonal exchange enriches both equilibrium ordering and dynamical critical behavior in a quantum Ising chain.

quant-pharXiv:2610.01167•Oct 2, 2026•0 citations

Criticality in correlated quantum matter

Angela Kopp, Sudip Chakravarty

arXiv:cond-mat/0503298•Nature Physics•Sep 29, 2005•122 citations

Dynamical spin-nematic correlation in a transverse field Ising chain with non-Hermitian Gamma interaction

Yu-Hong Yan, Ran Wang, Kun-Liang Zhang

We investigate the effect of non-Hermitian Gamma interaction on the phase transitions and magnetic correlations for the transverse field Ising chain. We demonstrate that apart from the gapped antiferromagnetic and paramagnetic phases, there is a gapless phase induced by parity-time symmetry breaking, where the system exhibits long-range and short-range spin-nematic correlations in different regions divided by the quantum critical line determined from the correlation function and the subsystem entanglement entropy. Furthermore, we reveal that the parity-time symmetry breaking leads to the emergence of dynamical spin-nematic correlation, which also suggests a way of characterizing the spin-nematic map through non-equilibrium dynamics. Our findings show rich quantum phases stem from the competition among the Ising interaction, transverse field and non-Hermitian Gamma interaction, as well as providing a scheme for generating spin-nematic correlation in the spin chain.

cond-mat.mes-hallCross-listedarXiv:2604.17700•Physical review. B./Physical review. B•Apr 21, 2026•0 citations

Microscopic theory revealing Ising criticality with distinct sublattice orders in extended Kitaev chains

Mandev Bhullar, Philip Richard, Hae-Young Kee

The one-dimensional transverse Ising model is a paradigmatic example of quantum criticality. In spin-orbit coupled systems, however, effective Ising interaction emerges from the interplay between the Kitaev ( K ) and Heisenberg ( J ) exchanges, and is accompanied by an additional bond-dependent interaction (Γ), leading to complex magnetic orders beyond the pure Ising limit. We first explore how the generic J - K -Γ model with four-fold screw symmetry in a spin-orbit-entangled chain manifests via sublattice order, and then test whether field-driven transitions retain Ising universality. We find sublattice-dependent magnetic order below the critical field and a distinct sublattice pattern persisting above it. Despite these complex magnetic ordered structures, the transition remains in the Ising universality class with central charge c = 1/2. Our work provides a route to the microscopic Hamiltonian and emergent Ising criticality while allowing microscopic physics of the sublattice orders to manifest at low and high fields. Application to Ising materials such as chains of Co 2+ ions is also discussed.

npj Quantum Materials•Sep 15, 2026•0 citations

The quantum Ising chain with a generalized defect

Uwe Grimm

arXiv:hep-th/0310089•Nuclear Physics B•Aug 1, 1990•29 citations
We investigate a transverse-field Ising chain with dimerized anisotropic Gamma interactions and demonstrate that, both in the absence and presence of Ising interactions, the competition between Gamma anisotropy and the transverse field gives rise to vector chiral order and dynamical quantum phase transitions. The phase diagram comprises positive and negative vector chiral phases and a paramagnetic phase, characterized by the vector spin chirality and the vector chiral order parameter. In the absence of Ising interactions, we identify a gapless critical line that exhibits no finite-size drift, along which the spin-spin correlations and subsystem entanglement entropy display behavior distinct from that of Ising criticality. Furthermore, we find that the critical times of dynamical quantum phase transitions form periodic or aperiodic sequences, depending on the quench path. Our findings highlight how dimerized off-diagonal exchange enriches both equilibrium ordering and dynamical critical behavior in a quantum Ising chain.
We investigate the effect of non-Hermitian Gamma interaction on the phase transitions and magnetic correlations for the transverse field Ising chain. We demonstrate that apart from the gapped antiferromagnetic and paramagnetic phases, there is a gapless phase induced by parity-time symmetry breaking, where the system exhibits long-range and short-range spin-nematic correlations in different regions divided by the quantum critical line determined from the correlation function and the subsystem entanglement entropy. Furthermore, we reveal that the parity-time symmetry breaking leads to the emergence of dynamical spin-nematic correlation, which also suggests a way of characterizing the spin-nematic map through non-equilibrium dynamics. Our findings show rich quantum phases stem from the competition among the Ising interaction, transverse field and non-Hermitian Gamma interaction, as well as providing a scheme for generating spin-nematic correlation in the spin chain.
The one-dimensional transverse Ising model is a paradigmatic example of quantum criticality. In spin-orbit coupled systems, however, effective Ising interaction emerges from the interplay between the Kitaev ( K ) and Heisenberg ( J ) exchanges, and is accompanied by an additional bond-dependent interaction (Γ), leading to complex magnetic orders beyond the pure Ising limit. We first explore how the generic J - K -Γ model with four-fold screw symmetry in a spin-orbit-entangled chain manifests via sublattice order, and then test whether field-driven transitions retain Ising universality. We find sublattice-dependent magnetic order below the critical field and a distinct sublattice pattern persisting above it. Despite these complex magnetic ordered structures, the transition remains in the Ising universality class with central charge c = 1/2. Our work provides a route to the microscopic Hamiltonian and emergent Ising criticality while allowing microscopic physics of the sublattice orders to manifest at low and high fields. Application to Ising materials such as chains of Co 2+ ions is also discussed.