arXiv subjects

C. J. Hamer

Publications and source records attributed to C. J. Hamer.

At least 37 records · Page 2Linked to original sources

arXiv2002

Persistent Currents in the Heisenberg chain with a weak link

The Heisenberg chain with a weak link is studied, as a simple example of a quantum ring with a constriction or defect. The Heisenberg chain is equivalent to a spinless electron gas under a Jordan-Wigner transformation. Using density matrix renormalization group and quantum Monte Carlo methods we calculate the spin/charge stiffness of the model, which determines the strength of the `persistent currents'. The stiffness is found to scale to zero in the weak link case, in agreement with renormalization group arguments of Eggert and Affleck, and Kane and Fisher.

cond-mat.str-el↗

arXiv2002

Two-Hole and Four-Hole Bound States in a t-J Ladder at half-filling

The two-hole excitation spectrum of the t-J ladder at half-filling is studied using linked-cluster series expansion methods. A rich spectrum of bound states emerges, particularly at small $t/J$. Their dispersion relations and coherence lengths are computed, along with the threshold behaviour as the bound states merge into the continuum. A class of 4-hole bound states is also studied, leading to the conclusion that phase separation occurs for $t/J \lesssim 0.5$, in agreement with other studies.

cond-mat.str-el↗

arXiv2002

Density Matrix Renormalisation Group Approach to the Massive Schwinger Model

The massive Schwinger model is studied, using a density matrix renormalisation group approach to the staggered lattice Hamiltonian version of the model. Lattice sizes up to 256 sites are calculated, and the estimates in the continuum limit are almost two orders of magnitude more accurate than previous calculations. Coleman's picture of `half-asymptotic' particles at background field theta = pi is confirmed. The predicted phase transition at finite fermion mass (m/g) is accurately located, and demonstrated to belong in the 2D Ising universality class.

hep-lat↗

arXiv2002

Density Matrix Renormalization Group Approach to the Massive Schwinger Model

The massive Schwinger model is studied, using a density matrix renormalization group approach to the staggered lattice Hamiltonian version of the model. Lattice sizes up to 256 sites are calculated, and the estimates in the continuum limit are almost two orders of magnitude more accurate than previous calculations. Coleman's picture of `half-asymptotic' particles at background field (theta = pi) is confirmed. The predicted phase transition at finite fermion mass (m/g) is accurately located, and demonstrated to belong in the 2D Ising universality class.

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

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

Linked Cluster Series Expansions for Two-Particle Bound States

We develop strong-coupling series expansion methods to study two-particle spectra of quantum lattice models. At the heart of the method lies the calculation of an effective Hamiltonian in the two-particle subspace. We explicitly consider an orthogonality transformation to generate this block diagonalization, and find that maintaining orthogonality is crucial for systems where the ground state and the two-particle subspace are characterized by identical quantum numbers. We discuss the solution of the two-particle Schrödinger equation by using a finite lattice approach in coordinate space or by an integral equation in momentum space. These methods allow us to precisely determine the low-lying excitation spectra of the models at hand, including all two-particle bound/antibound states. Further, we discuss how to generate series expansions for the dispersions of the bound/antibound states. These allow us to employ series extrapolation techniques, whereby binding energies can be determined even when the expansion parameters are not small. We apply the method to the (1+1)D transverse Ising model and the two-leg spin-$\case 1/2$ Heisenberg ladder. For the latter model, we also calculate the coherence lengths and determine the critical properties where bound states merge with the two-particle continuum.

cond-mat.str-el↗

arXiv2000

Deconfinement Transition and Bound States in Frustrated Heisenberg Chains: Regimes of Forced and Spontaneous Dimerization

We use recently developed strong-coupling expansion methods to study the two-particle spectra for the frustrated alternating Heisenberg model, consisting of an alternating nearest neighbor antiferromagnetic exchange and a uniform second neighbor antiferromagnetic exchange. Starting from the limit of weakly coupled dimers, we develop high order series expansions for the effective Hamiltonian in the two-particle subspace. In the limit of a strong applied dimerization, we calculate accurately various properties of singlet and triplet bound states and quintet antibound states. We also develop series expansions for bound state energies in various sectors, which can be extrapolated using standard methods to cases where the external bond-alternation goes to zero. We study the properties of singlet and triplet bound states in the latter limit and suggest a crucial role for the bound states in the unbinding of triplets and deconfinement of spin-half excitations.

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

Green's Function Monte Carlo approach to SU(3) Yang-Mills theory in (3+1)D

A 'forward walking' Green's Function Monte Carlo algorithm is used to obtain expectation values for SU(3) lattice Yang-Mills theory in (3+1) dimensions. The ground state energy and Wilson loops are calculated, and the finite-size scaling behaviour is explored. Crude estimates of the string tension are derived, which agree with previous results at intermediate couplings; but more accurate results for larger loops will be required to establish scaling behaviour at weak coupling.

hep-lat↗

arXiv2000

Strong-Coupling Expansions for Multiparticle Excitations: Continuum and Bound States

We present a new linked cluster expansion for calculating properties of multiparticle excitation spectra to high orders. We use it to obtain the two-particle spectra for systems of coupled spin-half dimers. We find that even for weakly coupled dimers the spectrum is very rich, consisting of many bound states. The number of bound states depends on both geometry of coupling and frustration. Many of the bound states can only be seen by going to sufficiently high orders in the perturbation theory, showing the extended character of the pair-attraction.

cond-mat.str-el↗

arXiv2000

Finite-Size Scaling in the transverse Ising Model on a Square Lattice

Energy eigenvalues and order parameters are calculated by exact diagonalization for the transverse Ising model on square lattices of up to 6x6 sites. Finite-size scaling is used to estimate the critical parameters of the model, confirming universality with the three-dimensional classical Ising model. Critical amplitudes are also estimated for both the energy gap and the ground-state energy.

cond-mat.stat-mech↗

arXiv2000

Green's Function Monte Carlo study of SU(3) lattice gauge theory in (3+1)D

A `forward walking' Green's Function Monte Carlo algorithm is used to obtain expectation values for SU(3) lattice Yang-Mills theory in (3+1) dimensions. The ground state energy and Wilson loops are calculated, and the finite-size scaling behaviour is explored. Crude estimates of the string tension are derived, which agree with previous results at intermediate couplings; but more accurate results for larger loops will be required to establish scaling behaviour at weak coupling.

hep-lat↗

arXiv1999

A New Finite-lattice study of the Massive Schwinger Model

A new finite lattice calculation of the low lying bound state energies in the massive Schwinger model is presented, using a Hamiltonian lattice formulation. The results are compared with recent analytic series calculations in the low mass limit, and with a new higher order non-relativistic series which we calculate for the high mass limit. The results are generally in good agreement with these series predictions, and also with recent calculations by light cone and related techniques.

hep-lat↗

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

Various series expansions for a Heisenberg antiferromagnet model for SrCu$_2$(BO$_3$)$_2$

We use a variety of series expansion methods at both zero and finite temperature to study an antiferromagnetic Heisenberg spin model proposed recently by Miyahara and Ueda for the quasi two-dimensional material SrCu$_2$(BO$_3$)$_2$. We confirm that this model exhibits a first-order quantum phase transition at T=0 between a gapped dimer phase and a gapless Néel phase when the ratio $x=J'/J$ of nearest and next-nearest neighbour interactions is varied, and locate the transition at $x_c=0.691(6)$. Using longer series we are able to give more accurate estimates of the model parameters by fitting to the high temperature susceptibility data.

cond-mat.str-el↗

arXiv1998

Meta-Plaquette Expansion for the Triplet Excitation Spectrum in CaV$_4$O$_9$

We study antiferromagnetic, $S=1/2$ Heisenberg models with nearest and second neighbor interactions on the one-fifth depleted square lattice which describes the spin degrees of freedom in the spin-gap system CaV$_4$O$_9$. The meta-plaquette expansion for the triplet excitation spectrum is extended to fifth order, and the results are compared with experimental data on CaV$_4$O$_9$. We attempt to locate the phase boundary between magnetically ordered and gapped phases.

cond-mat.str-el↗