Duality and ground-state phase diagram for the quantum XYZ model with arbitrary spin $s$ in one spatial dimensionDuality and ground-state phase diagram for the quantum XYZ model with arbitrary spin $s$ in one spatial dimension

Qian‐Qian Shi, Sheng-Hao Li, Huan-Qiang Zhou

Five duality transformations are unveiled for the quantum XYZ model with arbitrary spin $s$ in one spatial dimension. The presence of these duality transformations drastically reduces the entire ground-state phase diagram to two {\it finite} regimes - the principal regimes, with all the other ten regimes dual to them. Combining with the determination of critical points from the conventional order parameter approach and/or the fidelity approach to quantum phase transitions, we are able to map out the ground-state phase diagram for the quantum XYZ model with arbitrary spin $s$ . This is explicitly demonstrated for $s=1/2,1,3/2$ and 2. As it turns out, all the critical points, with central charge $c=1$ , are self-dual under a respective duality transformation for half-integer as well as integer spin $s$ . However, in the latter case, the presence of the so-called symmetry protected topological phase, i.e., the Haldane phase, results in extra lines of critical points with central charge $c=1/2$ , which is not self-dual under any duality transformation.Five duality transformations are unveiled for the quantum XYZ model with arbitrary spin $s$ in one spatial dimension. The presence of these duality transformations drastically reduces the entire ground-state phase diagram to two {\it finite} regimes - the principal regimes, with all the other ten regimes dual to them. Combining with the determination of critical points from the conventional order parameter approach and/or the fidelity approach to quantum phase transitions, we are able to map out the ground-state phase diagram for the quantum XYZ model with arbitrary spin $s$. This is explicitly demonstrated for $s=1/2,1,3/2$ and 2. As it turns out, all the critical points, with central charge $c=1$, are self-dual under a respective duality transformation for half-integer as well as integer spin $s$. However, in the latter case, the presence of the so-called symmetry protected topological phase, i.e., the Haldane phase, results in extra lines of critical points with central charge $c=1/2$, which is not self-dual under any duality transformation.

arXiv:1803.03935Mar 11, 20180 citations

Duality and ground-state phase diagram for the quantum XYZ model with arbitrary spin s in one spatial dimension

Qian‐Qian Shi, Sheng-Hao Li, Huan-Qiang Zhou

Abstract Five duality transformations are unveiled for the quantum XYZ model with arbitrary spin s in one spatial dimension. The presence of these duality transformations, together with an extra Hamiltonian symmetry, drastically reduce the entire ground-state phase diagram to two finite regimes—the principal regimes, with all the other ten regimes dual to them. Combining with the determination of critical points from the conventional order parameter approach and/or the fidelity approach to quantum phase transitions, we are able to map out the ground-state phase diagram for the quantum XYZ model with arbitrary spin s . This is explicitly demonstrated for s = 1 / 2 , 1 , 3 / 2 and 2. As it turns out, all the critical points, with central charge c = 1 , are self-dual for half-integer as well as integer spin s . However, in the latter case, the presence of the Haldane phase results in extra lines of critical points with central charge c = 1 / 2 , which are not self-dual.Abstract Five duality transformations are unveiled for the quantum XYZ model with arbitrary spin s in one spatial dimension. The presence of these duality transformations, together with an extra Hamiltonian symmetry, drastically reduce the entire ground-state phase diagram to two finite regimes—the principal regimes, with all the other ten regimes dual to them. Combining with the determination of critical points from the conventional order parameter approach and/or the fidelity approach to quantum phase transitions, we are able to map out the ground-state phase diagram for the quantum XYZ model with arbitrary spin s . This is explicitly demonstrated for s = 1 / 2 , 1 , 3 / 2 and 2. As it turns out, all the critical points, with central charge c = 1 , are self-dual for half-integer as well as integer spin s . However, in the latter case, the presence of the Haldane phase results in extra lines of critical points with central charge c = 1 / 2 , which are not self-dual.

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Duality and ground-state phase diagram for the quantum XYZ model with arbitrary spin

s

in one spatial dimension

Five duality transformations are unveiled for the quantum XYZ model with arbitrary spin

s

in one spatial dimension. The presence of these duality transformations drastically reduces the entire ground-state phase diagram to two {\it finite} regimes - the principal regimes, with all the other ten regimes dual to them. Combining with the determination of critical points from the conventional order parameter approach and/or the fidelity approach to quantum phase transitions, we are able to map out the ground-state phase diagram for the quantum XYZ model with arbitrary spin

s

. This is explicitly demonstrated for

s=1/2,1,3/2

and 2. As it turns out, all the critical points, with central charge

c=1

, are self-dual under a respective duality transformation for half-integer as well as integer spin

s

. However, in the latter case, the presence of the so-called symmetry protected topological phase, i.e., the Haldane phase, results in extra lines of critical points with central charge

c=1/2

, which is not self-dual under any duality transformation.