arXiv subjects

Zheng Weihong

Publications and source records attributed to Zheng Weihong.

At least 19 recordsLinked to original sources

arXiv2006

A modified triplet-wave expansion method applied to the alternating Heisenberg chain

An alternative triplet-wave expansion formalism for dimerized spin systems is presented, a modification of the 'bond operator' formalism of Sachdev and Bhatt. Projection operators are used to confine the system to the physical subspace, rather than constraint equations. The method is illustrated for the case of the alternating Heisenberg chain, and comparisons are made with the results of dimer series expansions and exact diagonalization. Some discussion is included of the phenomenon of 'quasiparticle breakdown', as it applies to the two-triplon bound states in this model.

cond-mat.str-el↗

arXiv2006

The J1-J2 model: First order phase transition versus deconfinement of spinons

We revisit the phase transition from the Néel ordered to a valence bond solid (VBS) state in the two-dimensional $J_1-J_2$ antiferromagnetic Heisenberg model. In the first part we address the question whether or not this transition could be an example of a second order phase transition due to a deconfinement of spinons. We give arguments based on series expansion and spin-wave theory that this is not the case and the transition is most likely first order. The method proposed here to detect first order phase transitions seems to be very sensitive and might be useful in other models as well. In the second part we analyze possible VBS patterns in the magnetically disordered phase based on numerical data for different susceptibilities, obtained in the ordered phase, which test the breaking of lattice symmetries. We conclude that a columnar dimerization pattern is the most likely candidate.

cond-mat.str-el↗

arXiv2005

The t-Jz ladder

The phase diagram of the two-leg t-Jz ladder is explored, using the density matrix renormalization group method. Results are obtained for energy gaps, electron density profiles and correlation functions for the half-filled and quarter-filled cases. The effective Lagrangian velocity parameter is shown to vanish at half-filling. The behaviour of the one-hole gap in the Nagaoka limit is investigated, and found to disagree with theoretical predictions. A tentative phase diagram is presented, which is quite similar to the full t-J ladder, but scaled up by a factor of about two in coupling. Near half-filling a Luther-Emery phase is found, which may be expected to show superconducting correlations, while near quarter-filling the system appears to be in a Tomonaga-Luttinger phase.

cond-mat.stat-mech↗

arXiv2005

The Union Jack model: a quantum spin model with frustration on the square lattice

A new quantum spin model with frustration, the `Union Jack' model on the square lattice, is analyzed using spin-wave theory. For small values of the frustrating coupling $α$, the system is N{\' e}el ordered as usual, while for large $α$ the frustration is found to induce a canted phase. The possibility of an intermediate spin-liquid phase is discussed.

cond-mat.str-el↗

arXiv2003

An Application of Feynman-Kleinert Approximants to the Massive Schwinger Model on a Lattice

A trial application of the method of Feynman-Kleinert approximants is made to perturbation series arising in connection with the lattice Schwinger model. In extrapolating the lattice strong-coupling series to the weak-coupling continuum limit, the approximants do not converge well. In interpolating between the continuum perturbation series at large fermion mass and small fermion mass, however, the approximants do give good results. In the course of the calculations, we picked up and rectified an error in an earlier derivation of the continuum series coefficients.

hep-lat↗

arXiv2001

Series Expansions for Variable Electron Density

We have developed a series expansion method for calculating the zero-temperature properties of lattice electron models for variable electron density, i.e. for finite doping away from the half-filled case. This is done by introducing particle fluctuation terms in both the unperturbed Hamiltonian and perturbation. The method is demonstrated by application to the 2-chain $t-J$ ladder, where we provide comparison with previous work as well as obtaining a number of new results.

cond-mat.str-el↗

arXiv2001

Critical dynamics of singlet and triplet excitations in strongly frustrated spin systems

New data for the two-dimensional J1-J2 model shows that the critical points for singlet and triplet excitations near J2/J1=0.38 are very close together, or coincident. We propose that this is a more general result: in strongly frustrated spin systems the critical dynamics of singlet and triplet excitations are closely related. An effective field theory for such a critical point, or points, is developed, and its implications discussed. The analysis suggests the existance of gapless or almost gapless singlet excitations in the magnetically disordered phase.

cond-mat.str-el↗

arXiv2001

The Phase Diagram of the Shastry-Sutherland Antiferromagnet

The Shastry-Sutherland model, which provides a representation of the magnetic properties of SrCu$_2$(BO$_3$)$_2$, has been studied by series expansion methods at T=0. Our results support the existence of an intermediate phase between the Néel long-range ordered phase and the short-range dimer phase. They provide strong evidence against the existence of helical order in the intermediate phase, and and somewhat less strong evidence against a plaquette-singlet phase. The nature of the intermediate phase thus remains elusive. It appears to be gapless, or nearly so.

cond-mat.str-el↗

arXiv2000

New quantum phase transitions in the two-dimensional J1-J2 model

We analyze the phase diagram of the frustrated Heisenberg antiferromagnet, the J1-J2 model, in two dimensions. Two quantum phase transitions in the model are already known: the second order transition from the Neel state to the spin liquid state at (J_2/J_1)_{c2}=0.38, and the first order transition from the spin liquid state to the collinear state at (J_2/J_1)_{c4}=0.60. We have found evidence for two new second order phase transitions: the transition from the spin columnar dimerized state to the state with plaquette type modulation at (J_2/J_1)_{c3}=0.50(2), and the transition from the simple Neel state to the Neel state with spin columnar dimerization at (J_2/J_1)_{c1}=0.34(4). We also present an independent calculation of (J_2/J_1)_{c2}=0.38 using a new approach.

cond-mat.str-el↗

arXiv2000

Numerical Studies of the two-leg Hubbard ladder

The Hubbard model on a two-leg ladder structure has been studied by a combination of series expansions at T=0 and the density-matrix renormalization group. We report results for the ground state energy $E_0$ and spin-gap $Δ_s$ at half-filling, as well as dispersion curves for one and two-hole excitations. For small $U$ both $E_0$ and $Δ_s$ show a dramatic drop near $t/t_{\perp}\sim 0.5$, which becomes more gradual for larger $U$. This represents a crossover from a "band insulator" phase to a strongly correlated spin liquid. The lowest-lying two-hole state rapidly becomes strongly bound as $t/t_{\perp}$ increases, indicating the possibility that phase separation may occur. The various features are collected in a "phase diagram" for the model.

cond-mat.str-el↗

arXiv2000

Local Spin Correlations in Heisenberg Antiferromagnets

We use linked cluster series expansion methods to estimate the values of various short distance correlation functions in $S=1/2$ Heisenberg antiferromagnets at T=0, for dimension $d=1,2,3$. The method incorporates the possibility of spontaneous symmetry breaking, which is manifest in $d=2,3$. The results are important in providing a test for approximate theories of the antiferromagnetic ground state.

cond-mat.str-el↗

arXiv2000

Low-energy singlet and triplet excitations in the spin-liquid phase of the two-dimensional J1-J2 model

We analyze the stability of the spontaneously dimerized spin-liquid phase of the frustrated Heisenberg antiferromagnet - the J1-J2 model. The lowest triplet excitation, corresponding to breaking of a singlet bond, is found to be stable in the region 0.38 < J2/J1 < 0.62. In addition we find a stable low-energy collective singlet mode, which is closely related to the spontaneous violation of the discrete symmetry. Both modes are gapped in the quantum disordered phase and become gapless at the transition point to the Neel ordered phase (J2/J1=0.38). The spontaneous dimerization vanishes at the transition and we argue that the disappearance of dimer order is related to the vanishing of the singlet gap. We also present exact diagonalization data on a small (4x4) cluster which indeed show a structure of the spectrum, consistent with that of a system with a four-fold degenerate (spontaneously dimerized) ground state.

cond-mat.str-el↗

arXiv1999

Spontaneous dimer order, excitation spectrum, and quantum phase transitions in the J1-J2 Heisenberg model

We overview some recent work and present new results on the ground state properties and the spectrum of excitations of the two-dimensional frustrated Heisenberg antiferromagnet. Spontaneous dimer order is present in the quantum disordered phase of this model. We study the stability and analyze the structure of the spectrum, including the two-particle singlet excitation branch throughout the disordered phase, as well as in the vicinity of the Neel critical point. The variation of the dimer order parameter is also given, and it is argued that near the critical point it reflects the presence of the low-energy singlet bound state.

cond-mat.str-el↗

arXiv1999

Studies of the t-J two-leg ladder via series expansions

Series expansions at T=0 are used to study properties of the half-filled $t-J$ ladder doped with one or two holes, and at quarter filling. Dispersion curves are obtained for one-hole symmetric and antisymmetric (bonding and antibonding) excitations and for the two-hole bound state. The line in the phase diagram which separates bound and unbound states is determined. For quarter filling we compute the ground state energy and estimate the location of the phase separation line. Comparisons with other numerical and analytical results are presented.

cond-mat.str-el↗

arXiv1999

Dimer Order with Striped Correlations in the J_1-J_2 Heisenberg Model

Ground state energies for plaquette and dimer order in the $J_1-J_2$ square-lattice spin-half Heisenberg model are compared using series expansion methods. We find that these energies are remarkably close to each other at intermediate values of $J_2/J_1$, where the model is believed to have a quantum disordered ground state. They join smoothly with those obtained from the Ising expansions for the 2-sublattice Néel-state at $J_2/J_1 \approx 0.4$, suggesting a second order transition from a Néel state to a quantum disordered state, whereas they cross the energy for the 4-sublattice ordered state at $J_2/J_1 \approx 0.6$ at a large angle, implying a first order transition to the 4-sublattice magnetic state. The strongest evidence that the plaquette phase is not realized in this model comes from the analysis of the series for the singlet and triplet excitation spectra, which suggest an instability in the plaquette phase. Thus, our study supports the recent work of Kotov et al, which presents a strong picture for columnar dimer order in this model. We also discuss the striped nature of spin correlations in this phase, with substantial resonance all along columns of dimers.

cond-mat.str-el↗

arXiv1998

Dynamical Transition from Triplets to Spinon Excitations: A Series Expansion Study of the $J_1-J_2-δ$ spin-half chain

We study the spin-half Heisenberg chain with alternating nearest neighbor interactions $J_1(1+δ)$ and $J_1(1-δ)$ and a uniform second neighbor interaction $J_2=y (1-δ)$ by series expansions around the limit of decoupled dimers ($δ=1$). By extrapolating to $δ=0$ and tuning $y$, we study the critical point separating the power-law and spontaneously dimerized phases of the spin-half antiferromagnet. We then focus on the disorder line $y=0.5$, $0\le δ\le 1$, where the ground states are known exactly. We calculate the triplet excitation spectrum, their spectral weights and wavevector dependent static susceptibility along this line. It is well known that as $δ\to 0$, the spin-gap is still non-zero but the triplets are replaced by spinons as the elementary excitations. We study this dynamical transition by analyzing the series for the spectral weight and the static susceptibility. In particular, we show that the spectral weight for the triplets vanishes and the static spin-susceptibility changes from a simple pole at imaginary wavevectors to a branch cut at the transition.

cond-mat.str-el↗

arXiv1998

Excitation spectrum and ground state properties of the S=1/2 Heisenberg ladder with staggered dimerization

We have studied the excitation spectrum of the $S=1/2$ quantum spin ladder with staggered dimerization by dimer series expansions, diagrammatic analysis of an effective interacting Bose gas of local triplets, and exact diagonalization of small clusters. We find that the model has two massive phases, with predominant inter-chain (rung) or intra-chain correlations. The transition from the rung dimer into the intra-chain dimer phase is characterized by softening of the triplet spectrum at $k=π$. The excitation spectrum as well as the spin correlations away from and close to the critical line are calculated. The location of the phase boundary is also determined.

cond-mat.str-el↗

arXiv1998

Phase diagram for a class of spin-half Heisenberg models interpolating between the square-lattice, the triangular-lattice and the linear chain limits

We study the spin-half Heisenberg models on an anisotropic two-dimensional lattice which interpolates between the square-lattice at one end, a set of decoupled spin-chains on the other end, and the triangular-lattice Heisenberg model in between. By series expansions around two different dimer ground states and around various commensurate and incommensurate magnetically ordered states, we establish the phase diagram for this model of a frustrated antiferromagnet. We find a particularly rich phase diagram due to the interplay of magnetic frustration, quantum fluctuations and varying dimensionality. There is a large region of the usual 2-sublattice Neél phase, a 3-sublattice phase for the triangular-lattice model, a region of incommensurate magnetic order around the triangular-lattice model, and regions in parameter space where there is no magnetic order. We find that the incommensurate ordering wavevector is in general altered from its classical value by quantum fluctuations. The regime of weakly coupled chains is particularly interesting and appears to be nearly critical.

cond-mat.str-el↗