arXiv subjects

U. Schollwoeck

Publications and source records attributed to U. Schollwoeck.

42 records · Page 3Linked to original sources

arXiv1998

Thermodynamics of frustrated quantum spin chains

We apply the transfer matrix DMRG to frustrated quantum spin chains, going down to T=0.025 while being in the thermodynamic limit. The incommensurability problem of exact diagonalization and the negative sign problem of quantum Monte Carlo vanish completely. To illustrate the method, we give results for chains with next-nearest neighbor frustration and the delta chain, which has been a testbed for many thermodynamic methods. By comparison, the DMRG proves to be an extremely powerful method for the old problem of the thermodynamics of frustrated systems.

cond-mat↗

arXiv1998

Absence of string order in the anisotropic S=2 Heisenberg antiferromagnet

We study an AFM Heisenberg S=2 quantum spin chain at T=0 with both interaction and on-site anisotropy, H = \sum_{i} {1/2}(S^{+}_{i}S^{-}_{i+1}+S^{-}_{i}S^{+}_{i+1}) +J^{z}S^{z}_{i}S^{z}_{i+1}+D(S^{z}_{i})^{2}. Contradictory scenarios exist for the S=2 anisotropic phase diagram, implying different mechanisms of the emergence of the classical limit. One main AKLT-based scenario predicts the emergence of a cascade of phase transitions not seen in the S=1 case. Another scenario is in favor of an almost classical phase diagram for S=2; the S=1 case then is very special with its dominant quantum effects. Numerical studies have not been conclusive. Using the DMRG, the existence of hidden topological order in the anisotropic S=2 chain is examined, as it distinguishes between the proposed scenarios. We show that the topological order is zero in the thermodynamical limit in all disordered phases, in particular in the new phase interposed between the Haldane and large-$D$ phases. This excludes the AKLT-model based scenario in favor of an almost classical phase diagram for the $S\leq 2$ spin chains.

cond-mat↗

arXiv1996

Variational and DMRG studies of the Frustrated Antiferromagnetic Heisenberg S=1 Quantum Spin Chain

We study a frustrated antiferromagnetic isotropic Heisenberg $S=1$ chain using a variational ansatz and the DMRG. At $α_D=0.284(1)$, there is a disorder point of the second kind, marking the onset of incommensurate correlations in the chain. At $α_L=0.3725(25)$ there is a Lifshitz point, at which the excitation spectrum develops a doubly degenerate structure. These points are the quantum remnants of the transition from antiferromagnetic to spiral order in the classical frustrated chain. At $α_T=0.7444(6)$ there is a first order phase transition from an AKLT phase to a next-nearest neighbor generalization of the AKLT model. At the transition, the string order parameter shows a discontinuous jump of 0.085 to 0; the correlation length and the gap are both finite at the transition. The problem of edge states in open frustrated chains is discussed at length.

cond-mat↗

arXiv1996

Spin ladders with nonmagnetic impurities

We investigate antiferromagnetic spin ladders with nonmagnetic impurities by variational and numerical (Lanczos and DMRG) methods. The interaction between the two unpaired spins opposite to the impurities is described by an effective exchange interaction $J_{eff}$, the magnitude of which depends on the impurity distance. The magnitude of $J_{eff}$ is different for unpaired spins at the edges of an open ladder and in the bulk. This difference is related to the different distribution of the unpaired spin into the bulk of the ladder. The numerical results are interpreted using matrix product states. Using the DMRG we calculate the spectrum of low-lying energy levels for up to 6 impurities and find that these spectra can be reproduced assuming pair interactions with an accuracy of better than 10\%. We discuss the filling of the ladder gap with impurity states and argue that in the thermodynamic limit the spin ladder with a finite concentration of impurities always shows a Curie susceptibility at low temperatures.

cond-mat↗

arXiv1995

Physical Meaning of the Affleck-Kennedy-Lieb-Tasaki S=1 Quantum spin chain

Most of the present understanding of the S=1 quantum spin chains displaying the Haldane gap is coming from the so-called valence-bond-solid Hamiltonian which has an exactly known ground state. We show that this point is characterized by the onset of short-range incommensurate spin correlations in the one-parameter family of Hamiltonians with biquadratic coupling: H = sum_i S_i S_{i+1} +alpha sum_i ( S_i S_{i+1} )^2. This gives a physical meaning to this special point. We establish precise values for the gaps, correlations, the string order parameter, and identify the VBS point as a *disorder* point in the sense of classical statistical mechanics. It is a quantum remnant of the classical transition between a ground state with long-range Néel order and a ground state with incommensurate long-range order.

cond-mat↗

arXiv1995

Haldane Gap and Hidden Order in the S=2 Antiferromagnetic Quantum Spin Chain

We have investigated Haldane's conjecture for the S=2 isotropic antiferromagnetic quantum spin chain with nearest-neighbor exchange J. Using a density matrix renormalization group algorithm for chains up to L=350 spins, we find in the thermodynamic limit a finite spin gap of Delta = 0.085(5)J and a finite spin-spin correlation length xi = 49(1) lattice spacings. We establish the ground state energy per bond to be E_0=-4.761248(1)J. We show that the ground state has a hidden topological order that is revealed in a nonlocal string correlation function. This means that the physics of the S=2 chain can be captured by a valence-bond solid description. We also observe effective free spin-1 states at the ends of an open S=2 chain.

cond-mat↗