We study the T = 0 frustrated phase of the 1D quantum spin-1 2 system with nearest-neighbour and next-nearest-neighbour isotropic exchange known as the Majumdar-Ghosh Hamiltonian. We first apply the coupled-cluster method of quantum many-body theory based on a spiral model state to obtain the ground state energy and the pitch angle. These results are compared with accurate numerical results using the density matrix renormalisation group method, which also gives the correlation functions. We also investigate the periodicity of the phase using the Marshall sign criterion. We discuss particularly the behaviour close to the phase transitions at each end of the frustrated phase.

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 θ = π 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.

We apply a recent adaptation of White's density matrix renormalisation group (DMRG) method to a simple quantum spin model, the dimerised XY chain, in order to assess the applicabilty of the DMRG to quantum systems at non-zero temperature. We find that very reasonable results can be obtained for the thermodynamic functions down to low temperatures using a very small basis set. Low temperature results are found to be most accurate in the case when there is a substantial energy gap.Since it's recent inception, White's denstiy matrix renormalisation group (DMRG) method has been established as the method of choice for determining static, low energy properties of one-dimensional quantum lattice systems [1]- [2]. Extensions to the calculation of dynamical properaties [3] and even to the study of low temperature properties of two dimensional systems [4] have been forthcoming. Moreover, Nishino's formulation of the DMRG for two dimensional classical systems [5] has paved the way for the study of one dimensional quantum systems at non-zero temperature. In this letter we present what is, to the best of our knowledge, the first application of the DMRG to the thermodynamics of a quantum system.The system that we consider is a simple spin chain model-the dimerised, S = 1/2, XY modelwhere S i is a spin-1/2 operator for site i on an (even) chain of N sites, with periodic boundary conditions. 0

The one-dimensional Holstein model of spinless fermions interacting with dispersionless phonons is studied using a new variant of the density matrix renormalization group. By examining various low-energy excitations of finite chains, the metal-insulator phase boundary is determined precisely and agrees with the predictions of strong coupling theory in the antiadiabatic regime and is consistent with renormalization group arguments in the adiabatic regime. The Luttinger liquid parameters, determined by finite-size scaling, are consistent with a Kosterlitz-Thouless transition. [S0031-9007(98)06342-X] PACS numbers: 71.10. Fd, 71.30. + h, 71.38. + i, 71.45.Lr The challenge of understanding superconductivity in fullerenes, bismuth oxides, and the high-T c cuprates has renewed interest in models of interacting electrons and phonons [1]. Unlike conventional metals these materials are not necessarily in the weak-coupling regime where perturbation theory can be used or the strong-coupling regime in which a polaronic treatment is possible [1]. Neither are they necessarily in the adiabatic regime in which characteristic phonon energies are much less than characteristic electronic energies. This challenge has led to numerical studies of the Holstein (or molecular crystal) model of electrons interacting with dispersionless phonons in infinite dimensions, in two dimensions, in one dimension, and on just two sites (see the references in [1,2]). The one-dimensional case is important because of the wide range of quasi-one-dimensional materials which undergo a Peierls or charge-density-wave (CDW) instability due to the electron-phonon interaction. Most theoretical treatments assume the adiabatic limit and treat the phonons in a mean-field approximation. However, it has been argued that in many CDW materials the quantum lattice fluctuations are important [3].In this Letter we present a study of the one-dimensional Holstein model of spinless fermions at half-filling using the density matrix renormalization group (DMRG). This model is particularly interesting because at a finite fermionphonon coupling there is a quantum phase transition from a Luttinger liquid (metallic) phase to an insulating phase with CDW long-range order [4,5]. This illustrates how quantum fluctuations can destroy the Peierls state. The Hamiltonian iswhere c i destroys a fermion on site i, a i destroys a local phonon of frequency v, t is the hopping integral, g is the fermion-phonon coupling, and a periodic chain of N sites is assumed. The phase transition occurs at a critical coupling g c separating metallic (0 # g # g c ) and CDW insulating phases ( g . g c ) [4,5]. In the strong coupling limit ( g 2 ¿ vt) (1) can be mapped onto the anisotropic, antiferromagnetic Heisenberg (XXZ) model [4] which is exactly soluble. The transition occurs at the spin isotropy point and is of the Kosterlitz-Thouless (KT) type, and the Luttinger liquid parameters can be found in the metallic phase [2].The phase diagram of (1) 2ptv͞g 2 is the mean-field energy gap) and is the ap...

Based on exact diagonalization and density matrix renormalization group method, we show that an anisotropic triangular lattice Heisenberg spin model has three distinct quantum phases. In particular, a spin-liquid phase is present in the weak interchain coupling regime, which is characterized by an anisotropic spin structure factor with an exponential-decay spin correlator along the weaker coupling direction, consistent with the Cs 2 CuCl 4 compounds. In the obtained phase diagram, the spin-liquid phase is found to persist up to a relatively large critical anisotropic coupling ratio JЈ / J = 0.78, which is stabilized by strong quantum fluctuations, with a parity symmetry distinct from two magnetic ordered states in the stronger coupling regime. Two-dimensional ͑2D͒ frustrated spin systems have attracted intensive studies as they may exhibit unconventional magnetic properties.1-4 The isotropic spin-1 / 2 Heisenberg antiferromagnet ͑HAFM͒ on a triangular lattice was a candidate for the realization of a disordered spin-liquid phase, 1 but it turns out to exhibit a three-sublattice antiferromagneticlong-range-order ͑AFLRO͒ as established by analytic [5][6][7][8] and numerical 5,9,10 studies. Among various spin models, a spin-liquid phase has been established for more geometrically frustrated systems on the Kagome lattice, 11,12 dimer models, 13 and models involving four spin exchange terms.14 The Heisenberg models on the square lattice with thirdnearest-neighbor couplings may also have a spin-liquid ground state as revealed by recent numerical studies based on density matrix renormalization group ͑DMRG͒ calculations. 15From the experimental point of view, the HAFM on an anisotropic triangular lattice is particularly interesting as it is directly relevant to the quantum magnet in the Cs 2 CuCl 4 compounds, 16-18 which may be described by a minimal model at half-filling ͑Ref. 19͒:Here S i are spin-1 / 2 operators, and J, JЈ ജ 0 are the nearestneighbor couplings along the chain ͑J͒ and the other two axes ͑JЈ͒ between different chains on a triangular lattice. Based on the variational Monte Carlo ͑VMC͒ method, a resonating valence bond ͑RVB͒ wave function was previously proposed 19 to describe the low-lying anisotropic spin excitation observed experimentally [16][17][18] in these systems, which suggests a gapless spin-liquid state. The model has also been studied by different analytic approaches such as spin wave theory ͑SWT͒, 6 large-S expansion, 8 as well as the series expansion. 20,21 These works have predicted magnetic ordered states at JЈ ജ 0.3J ± 0.03J side, while the magnetic order vanishes on the smaller JЈ side suggesting a disordered phase. The recent series expansion study by Zheng et al. 21 has further indicated that quantum renormalizations strongly enhance the one dimensionality of the spectra, which implies that a more accurate description of quantum effects is needed. Thus exact calculations with taking into account all the quantum fluctuations are highly desirable in order to further establish of exi...