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Physical review. B, Condensed matter

Phase transition in a U(1)-lattice-gauge system derived from a weakly three-dimensionalt-Jmodel

Yasuko Munehisa

Published Jul 1, 1992• 0 citations
Publisher

Abstract

We numerically study a U(1)-lattice-gauge system, which is an effective model of the Ginzburg-Landau-type obtained from the t-J model of electrons. The model, which we call the ``GL'' model for short, is composed of link variables interpreted as a nearest-neighbor hole-pair field bounded by the singlet spin pairs. We concentrate our attention on the weakly three-dimensional case in which the electron hopping in the third direction is suppressed compared to other directions. When we simulate the model on an ${\mathit{L}}^{3}$ lattice, we therefore actually treat a system of L loosely coupled layers each of which is of size ${\mathit{L}}^{2}$. Monte Carlo simulations are done on ${12}^{3}$, ${20}^{3}$, and ${30}^{3}$ lattices with the electron density slightly less than the half-filled one (the doping parameter \ensuremath{\delta} is mostly 0.06) and with the ratio of the interlayer-to-intralayer hopping parameter ranging between 0.1 and 0.9. We observe cusplike behavior of the specific heat, which indicates a phase transition due to the spontaneous breaking of a global symmetry of the GL model. An average link variable in one direction within the layers turns out to serve as a nice order parameter of the transition. The transition temperature ${\mathit{T}}_{\mathit{c}}$ decreases as the interlayer hopping of the electrons increases. Results on some expectation values, which indicate strong correlations between link variables below ${\mathit{T}}_{\mathit{c}}$, are also presented.

DOI
10.1103/physrevb.46.279

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We numerically study a U(1)-lattice-gauge system, which is an effective model of the Ginzburg-Landau-type obtained from the t-J model of electrons. The model, which we call the ``GL'' model for short, is composed of link variables interpreted as a nearest-neighbor hole-pair field bounded by the singlet spin pairs. We concentrate our attention on the weakly three-dimensional case in which the electron hopping in the third direction is suppressed compared to other directions. When we simulate the model on an L3{\mathit{L}}^{3}L3 lattice, we therefore actually treat a system of L loosely coupled layers each of which is of size L2{\mathit{L}}^{2}L2. Monte Carlo simulations are done on 123{12}^{3}123, 203{20}^{3}203, and 303{30}^{3}303 lattices with the electron density slightly less than the half-filled one (the doping parameter \ensuremath{\delta} is mostly 0.06) and with the ratio of the interlayer-to-intralayer hopping parameter ranging between 0.1 and 0.9. We observe cusplike behavior of the specific heat, which indicates a phase transition due to the spontaneous breaking of a global symmetry of the GL model. An average link variable in one direction within the layers turns out to serve as a nice order parameter of the transition. The transition temperature Tc{\mathit{T}}_{\mathit{c}}Tc​ decreases as the interlayer hopping of the electrons increases. Results on some expectation values, which indicate strong correlations between link variables below Tc{\mathit{T}}_{\mathit{c}}Tc​, are also presented.
We study a system of doped antiferromagnet in three dimensions at finite temperatures using the ttt-JJJ model, a canonical model of strongly correlated electrons. We employ the slave-fermion representation of electrons, in which an electron is described as a composite of a charged spinless holon and a chargeless spinon. We introduce two kinds of U(1) gauge fields on links as auxiliary fields, one describing resonating valence bonds of antiferromagnetic nearest-neighbor spin pairs and the other for nearest-neighbor hopping amplitudes of holons and spinons in the ferromagnetic channel. To perform a numerical study of the system, we integrate out the fermionic holon field by using the hopping expansion in powers of the hopping amplitude, which is legitimate for the region in and near the insulating phase. The resultant effective model is described in terms of bosonic spinons, two U(1) gauge fields, and a collective field for hole pairs. We study this model by means of Monte Carlo simulations, calculating the specific heat, spin correlation functions, and instanton densities. We obtain a phase diagram in the hole concentration-temperature plane, which is in good agreement with that observed recently for clean and homogeneous underdoped samples.
We present an exact diagonalization study of bilayer clusters of the t-J model. Our results indicate a crossover between two markedly different regimes which occurs when the ratio ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$/J between interlayer and intralayer exchange constants increases: for small ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$/J the data suggest the development of three-dimensional antiferromagnetic correlations without appreciable degradation of the intralayer spin order and the dx2{\mathit{d}}_{\mathit{x}}^{2}dx2​-y2{\mathit{y}}^{2}y2 hole pairs within the planes persist. For larger values of ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$/J local singlets along the interlayer bonds dominate, leading to an almost complete suppression of the intralayer spin correlation and the breaking of the intralayer hole pairs. The ground state with two holes in this regime has s-like symmetry. We present data for static spin correlation function, magnetic structure factor, and spin gap. We calculate the momentum distribution and electronic spectral function of the ``local singlet state'' realized for large ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$/J, and show that it deviates markedly from that of a single layer, making it an implausible candidate for modeling high-temperature superconductors.
We study the phase diagram and critical behaviors of three-dimensional lattice Z2{\mathbb{Z}}_{2}Z2​-gauge NNN-vector models, in which an NNN-component real field is minimally coupled with Z2{\mathbb{Z}}_{2}Z2​-gauge link variables. These models are invariant under global O(N\mathrm{O}(NO(N) and local Z2{\mathbb{Z}}_{2}Z2​ transformations. They present three phases characterized by the spontaneous breaking of the global O(N\mathrm{O}(NO(N) symmetry and by the different topological properties of the Z2{\mathbb{Z}}_{2}Z2​-gauge correlations. We address the nature of the three transition lines separating the three phases. The theoretical predictions are supported by numerical finite-size scaling analyses of Monte Carlo data for the N=2N=2N=2 model. In this case, continuous transitions can be observed along both transition lines where the NNN-component spins order, in the regimes of small and large inverse gauge coupling KKK. Even though these continuous transitions belong to the same XYXYXY universality class, their critical modes turn out to be different. When the gauge variables are disordered (small KKK), the relevant order-parameter field is a gauge-invariant bilinear combination of the vector field. On the other hand, when the gauge variables are ordered (large KKK), the order-parameter field is the gauge-dependent NNN-vector field, whose critical behavior can only be probed by using a stochastic gauge fixing that reduces the gauge freedom.
We have used exact diagonalization and quantum Monte Carlo methods to study the one-dimensional t-J model including the three-site hopping term derived from the strong-coupling limit of the Hubbard model. The three-site term may be important to superconducting correlations since it allows direct hopping of local singlet electron pairs. The phase diagram is determined for several values of the strength of the three-site term and compared with that of the t-J and Hubbard models. Phase separation, which exists in the t-J model, is suppressed. In the low electron density region the formation of local singlet electron pairs is enhanced, leading to stronger superconducting correlations even for values J/t2. A large spin gap region extends from low electron densities up to high densities. In the low hole density region the superconducting correlations are suppressed at J/t>2.8 in spite of enhanced pair formation. This is because the three-site term, while enhancing the formation of electron pairs, leads to a repulsion between holes.
We derive an effective Hamiltonian for the one-dimensional Hubbard-Holstein model, valid in a regime of both strong electron-electron (e-e) and electron-phonon (e-ph) interactions and in the nonadiabatic limit ($t/{\ensuremath{\omega}}_{0}\ensuremath{\le}1$), by using a nonperturbative approach. We obtain the phase diagram at quarter filling by employing a modified Lanczos method and studying various density-density correlations. The spin-spin AF (antiferromagnetic) interactions and nearest-neighbor repulsion, resulting from the e-e and the e-ph interactions, respectively, are the dominant terms (compared to hopping) and compete to determine the various correlated phases. As e-e interaction (U/t)(U/t)(U/t) is increased, the system transits from an AF cluster to a correlated singlet phase through a discontinuous transition at all strong e-ph couplings $2\ensuremath{\le}g\ensuremath{\le}3$ considered. At higher values of U/tU/tU/t and moderately strong e-ph interactions ($2\ensuremath{\le}g\ensuremath{\le}2.6$), the singlets break up to form an AF order and then to a paramagnetic order all in a single sublattice; whereas at larger values of ggg (>>>2.62.62.6), the system jumps directly to the spin disordered charge-density-wave (CDW) phase.
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