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Phase diagram of the t-J model: A semiclassical calculation

Jianping Lü, W. Barford

Published May 12, 2023• 0 citations
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Abstract

The results of a semiclassical variational calculation of the t-J model are presented. The generalized staggered flux phases are introduced. It is found that these flux phases are stable for a large parameter range of the phase diagram. An interesting feature of these flux phases is that for small doping they have the best potential energy and for larger doping they have the best kinetic energy. It is also found that only those flux phases that do not break the local time reversal and parity symmetries are energetically favored. For sufficiently small J/t and doping the spiral phase is stable.

DOI
10.17615/gc29-9t14

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The results of a semiclassical variational calculation of the t-J model are presented. The generalized staggered flux phases are introduced. It is found that these flux phases are stable for a large parameter range of the phase diagram. An interesting feature of these flux phases is that for small doping they have the best potential energy and for larger doping they have the best kinetic energy. It is also found that only those flux phases that do not break the local time reversal and parity symmetries are energetically favored. For sufficiently small J/t and doping the spiral phase is stable.
The results of a semiclassical variational calculation of the t-J model are presented. The generalized staggered flux phases are introduced. It is found that these flux phases are stable for a large parameter range of the phase diagram. An interesting feature of these flux phases is that for small doping they have the best potential energy and for larger doping they have the best kinetic energy. It is also found that only those flux phases that do not break the local time reversal and parity symmetries are energetically favored. For sufficiently small J/t and doping the spiral phase is stable.
We calculate the energy of flux states described by Slater determinants of single-particle levels in a uniform magnetic field with p/q flux quanta per plaquette and with no double occupancy. We find the exchange energy of flux states is lower than that of the Gutzwiller wave function by 10%--20%. The minimum kinetic energy is obtained by introducing phases associated with the holes. The phases are calculated by mapping onto a classical frustrated XY model. At 10% doping, the 1/2 flux state (\ensuremath{\pi} phase) is stabilized for the parameter regime J/t\ensuremath{\gtrsim}0.2. At about 20% doping, the time-reversal-breaking (1/3 flux state has the lowest energy for J/t\ensuremath{\gtrsim}1.0.
We study the stability of the time-reversal symmetry breaking staggered-flux phase of a single band Hubbard model, within the variational cluster approach. For intermediate and small values of the interaction UUU, we find metastable solutions for the staggered-flux phase, with a maximum current per bond at $U\ensuremath{\approx}3.2$. However, allowing for antiferromagnetic and superconducting long-range order it turns out that in the region at and close to half filling the antiferromagnetic phase is the most favorable energetically. The effect of nearest-neighbor interaction is also considered. Our results show that a negative nearest-neighbor interaction and finite doping favors the stability of the staggered-flux phase. We also present preliminary results for the three-band Hubbard model obtained with a restricted set of variational parameters. For this case, no spontaneous time-reversal symmetry breaking phase is found in our calculations.
The authors have numerically evaluated the energy of the staggered flux phase state (SFP), the d-wave resonating valence bond state, and the mixed SFP and d-wave state (SFP+d) of the extended t-J model at various hole densities ( delta ). The flux per plaquette and the size of the d-wave gap are taken as variational parameters. The calculation includes the kinetic energy, spin energy, the effective hole-hole interaction and the three-site pair-hopping term. They found that the SFP is stable against the projected Fermi liquid up to delta approximately=20%. For moderately large J, J/t>or=0.4, the SFP+d state may be favoured against the pure d-wave state but only at very low hole density ( delta approximately 20%). These calculations show that the pure SFP state is never the ground state at hole densities of experimental interest.
We analyze a class of mean-field flux phases of the slave boson t-J model, and present a finite-temperature phase diagram. The mean-field theory arises from a decomposition of the four-fermion terms into exchange, pairing, and direct terms, using Hubbard-Stratonovich fields. We find numerically that at low doping staggered flux phases are energetically favorable over the d-wave-pairing state. Very close to half filling a \ensuremath{\pi}-flux phase becomes stable. The occurrence of flux phases suppresses the pairing gap transition temperature.