We have studied the stability of the Fermi-liquid phase of a square-lattice tight-binding model with respect to the spontaneous generation of magnetic flux and orbital magnetization. An energy density of the form 1/2 ${\mathit{KB}}^{2}$ is associated with the magnetic field B, and the phase diagram is investigated as a function of K, temperature T, and density or chemical potential \ensuremath{\mu}. For K\ensuremath{\ne}0 and density near half filling, the system condenses below a critical temperature into a \ensuremath{\surd}2 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}2 antiferromagnetic flux phase in which the spontaneously generated flux alternates in sign in a checkerboard pattern. Farther from half filling and for K\ensuremath{\ne}0, the \ensuremath{\surd}2 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}2 pattern is replaced by an incommensurate flux phase in which the spatial periodicity of the spatially modulated flux is in general an irrational multiple of the lattice constant. At zero temperature for densities off half filling, the commensurate flux phase with uniform flux density equal to the particle density is the lowest-energy state of those considered at sufficiently small values of K. We also relate the Fermi-liquid instabilities of this gauge-invariant tight-binding (t-\ensuremath{\varphi}) model at nonzero K/t to those of the large-N t-J model at nonzero t/J, and thereby predict the existence of similar flux-phase instabilities in the latter model.We have studied the stability of the Fermi-liquid phase of a square-lattice tight-binding model with respect to the spontaneous generation of magnetic flux and orbital magnetization. An energy density of the form 1/2${\mathit{KB}}^{2}$ is associated with the magnetic field B, and the phase diagram is investigated as a function of K, temperature T, and density or chemical potential \ensuremath{\mu}. For K\ensuremath{\ne}0 and density near half filling, the system condenses below a critical temperature into a \ensuremath{\surd}2 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}2 antiferromagnetic flux phase in which the spontaneously generated flux alternates in sign in a checkerboard pattern. Farther from half filling and for K\ensuremath{\ne}0, the \ensuremath{\surd}2 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}2 pattern is replaced by an incommensurate flux phase in which the spatial periodicity of the spatially modulated flux is in general an irrational multiple of the lattice constant. At zero temperature for densities off half filling, the commensurate flux phase with uniform flux density equal to the particle density is the lowest-energy state of those considered at sufficiently small values of K. We also relate the Fermi-liquid instabilities of this gauge-invariant tight-binding (t-\ensuremath{\varphi}) model at nonzero K/t to those of the large-N t-J model at nonzero t/J, and thereby predict the existence of similar flux-phase instabilities in the latter model.

Physical review. B, Condensed matterNov 1, 199012 citations

Flux Phases in the t — J Model

Thomas Maurice Rice

Recent Progress in Many-Body TheoriesJan 1, 19904 citations

A generalized flux phase for the t-J model

D. Peter, Didier Mayou, M. Cyrot

Physica C SuperconductivityDec 1, 19910 citations

Charge excitation and the normal-state transport properties in the flux-binding phase of thet-Jmodel

Zheng-Yu Weng, D. N. Sheng, C. S. Ting

Elementary excitations are discussed in the flux-binding phase [Weng, Sheng, and Ting, Phys. Rev. B 49, 607 (1994)] of the t-J model. It is shown that the density and current constraints in the gauge-theory description will dramatically modify the charge excitations. An effective Lagrangian for the normal state of the flux-binding phase is derived, and based on it the transport properties are studied. We find that the resistivity is linearly temperature dependent with a relaxation rate \ensuremath{\Elzxh}/\ensuremath{\tau}\ensuremath{\simeq}2 ${\mathit{k}}_{\mathit{B}}$ T, and the Hall coefficient involves a second relaxation rate with the cotangent Hall angle following a ${\mathit{T}}^{2}$ law. Furthermore, the thermopower exhibits a strong doping dependence. All these features are in good agreement with the transport measurements of the high- ${\mathit{T}}_{\mathit{c}}$ copper oxide compounds.Elementary excitations are discussed in the flux-binding phase [Weng, Sheng, and Ting, Phys. Rev. B 49, 607 (1994)] of the t-J model. It is shown that the density and current constraints in the gauge-theory description will dramatically modify the charge excitations. An effective Lagrangian for the normal state of the flux-binding phase is derived, and based on it the transport properties are studied. We find that the resistivity is linearly temperature dependent with a relaxation rate \ensuremath{\Elzxh}/\ensuremath{\tau}\ensuremath{\simeq}2${\mathit{k}}_{\mathit{B}}$T, and the Hall coefficient involves a second relaxation rate with the cotangent Hall angle following a ${\mathit{T}}^{2}$ law. Furthermore, the thermopower exhibits a strong doping dependence. All these features are in good agreement with the transport measurements of the high-${\mathit{T}}_{\mathit{c}}$ copper oxide compounds.

Physical review. B, Condensed matterOct 1, 19944 citations

Signatures of a staggered-flux phase in the t−J model with two holes on a 32-site lattice

P. W. Leung

We study the relevance of the staggered-flux phase in the $t\ensuremath{-}J$ model using a system with two holes on a 32-site lattice with periodic boundary conditions. We find a staggered-flux pattern in the current-current correlation in the lowest energy d-wave state where there is mutual attraction between the holes. This staggered correlation decays faster with distance when the hole binding becomes stronger. This is in complete agreement with a recent study by Ivanov, Lee, and Wen [Phys. Rev. Lett. 84, 3958 (2000)] based on the SU(2) theory, and strongly suggests that the staggered-flux phase is a key ingredient in the $t\ensuremath{-}J$ model. We further show that this staggered-flux pattern does not exist in a state where the holes repel each other. Correlations of the chirality operator ${\mathbf{S}}_{1}\ensuremath{\cdot}({\mathbf{S}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbf{S}}_{3})$ show that the staggered pattern of the chirality is closely tied to the holes.We study the relevance of the staggered-flux phase in the $t\ensuremath{-}J$ model using a system with two holes on a 32-site lattice with periodic boundary conditions. We find a staggered-flux pattern in the current-current correlation in the lowest energy d-wave state where there is mutual attraction between the holes. This staggered correlation decays faster with distance when the hole binding becomes stronger. This is in complete agreement with a recent study by Ivanov, Lee, and Wen [Phys. Rev. Lett. 84, 3958 (2000)] based on the SU(2) theory, and strongly suggests that the staggered-flux phase is a key ingredient in the $t\ensuremath{-}J$ model. We further show that this staggered-flux pattern does not exist in a state where the holes repel each other. Correlations of the chirality operator ${\mathbf{S}}_{1}\ensuremath{\cdot}({\mathbf{S}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbf{S}}_{3})$ show that the staggered pattern of the chirality is closely tied to the holes.

arXiv:cond-mat/0007068Physical review. B, Condensed matterSep 1, 200054 citations

Properties of flux phases in the t-J model

Masao Ogata, Thomas Maurice Rice

Journal of Magnetism and Magnetic MaterialsDec 1, 19900 citations

{\mathit{KB}}^{2}

is associated with the magnetic field B, and the phase diagram is investigated as a function of K, temperature T, and density or chemical potential \ensuremath{\mu}. For K\ensuremath{\ne}0 and density near half filling, the system condenses below a critical temperature into a \ensuremath{\surd}2 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}2 antiferromagnetic flux phase in which the spontaneously generated flux alternates in sign in a checkerboard pattern. Farther from half filling and for K\ensuremath{\ne}0, the \ensuremath{\surd}2 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}2 pattern is replaced by an incommensurate flux phase in which the spatial periodicity of the spatially modulated flux is in general an irrational multiple of the lattice constant. At zero temperature for densities off half filling, the commensurate flux phase with uniform flux density equal to the particle density is the lowest-energy state of those considered at sufficiently small values of K. We also relate the Fermi-liquid instabilities of this gauge-invariant tight-binding (t-\ensuremath{\varphi}) model at nonzero K/t to those of the large-N t-J model at nonzero t/J, and thereby predict the existence of similar flux-phase instabilities in the latter model.

{\mathit{k}}_{\mathit{B}}

T, and the Hall coefficient involves a second relaxation rate with the cotangent Hall angle following a

{\mathit{T}}^{2}

law. Furthermore, the thermopower exhibits a strong doping dependence. All these features are in good agreement with the transport measurements of the high-

{\mathit{T}}_{\mathit{c}}

copper oxide compounds.