Thermodynamic Limit of Density Matrix Renormalization

Östlund, Stellan; Rommer, Stefan

doi:10.1103/physrevlett.75.3537

Cited by 1,010 publications

(1,208 citation statements)

References 17 publications

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“…One means of extending the DMRG method to classical systems is by mapping a twodimensional (2D) classical system to a 1D quantum spin system [59] by use of the transfer matrix [60] together with the Suzuki-Trotter formula [61]. Such a method was developed by Nishino et al for an infinite lattice, and is called the product-wave-function renormalization group (PWFRG) method [62]- [64]. For the calculations in the present paper, we also adopt the PWFRG method.…”

Section: Model Hamiltonianmentioning

confidence: 99%

Non-universal equilibrium crystal shape results from sticky steps

Akutsu¹

2011

J. Phys.: Condens. Matter

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Abstract. The anisotropic surface free energy, Andreev surface free energy, and equilibrium crystal shape (ECS) z = z(x, y) are calculated numerically using a transfer matrix approach with the density matrix renormalization group (DMRG) method. The adopted surface model is a restricted solid-on-solid (RSOS) model with "sticky" steps, i.e., steps with a point-contact type attraction between them (p-RSOS model). By analyzing the results, we obtain a first-order shape transition on the ECS profile around the (111) facet; and on the curved surface near the (001) facet edge, we obtain shape exponents having values different from those of the universal GruberMullins-Pokrovsky-Talapov (GMPT) class. In order to elucidate the origin of the non-universal shape exponents, we calculate the slope dependence of the mean step height of "step droplets" (bound states of steps) n(p) using the Monte Carlo method, where p = (∂z/∂x, ∂z/∂y), and · represents the thermal average. Using the result of the |p| dependence of n(p) , we derive a |p|-expanded expression for the non-universal surface free energy f eff (p), which contains quadratic terms with respect to |p|. The first-order shape transition and the non-universal shape exponents obtained by the DMRG calculations are reproduced thermodynamically from the non-universal surface free energy f eff (p).

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Section: Model Hamiltonianmentioning

confidence: 99%

Non-universal equilibrium crystal shape results from sticky steps

Akutsu¹

2011

J. Phys.: Condens. Matter

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“…The theory of entanglement has yielded tools to quantify quantum correlation, 3 as well as a theoretical framework for the understanding of the DMRG, 4 and the development of algorithms to deal with problems in higher dimensions, 5 and also to describe time evolution, systems at finite temperature and quantum dissipation. 6,7 DMRG is a variational method over the class of matrix product states, 4,8 which correspond to the one-dimensional ͑1D͒ realization of the more general projected entangled pair states ͑PEPS͒ introduced in Ref. 5.…”

Section: Introductionmentioning

confidence: 99%

Renormalization algorithm for the calculation of spectra of interacting quantum systems

2006

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We present an algorithm for the calculation of eigenstates with definite linear momentum in quantum lattices. Our method is related to the density matrix renormalization group, and makes use of the distribution of multipartite entanglement to build variational wave functions with translational symmetry. The algorithm is applied to the study of bilinear-biquadratic S = 1 chains, in particular to the region of phase space between the dimerized and ferromagnetic phases.

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“…The observation that for physical systems only minor part of the Hilbert space is involved [30], resulted in the rapid development of numerical methods based on a variational method within the space of MPS. It corresponds to assigning a finite entanglement content to spins in the ground state.…”

Section: Time Evolution Of Matrix Product Statesmentioning

confidence: 99%

Relaxation Dynamics in the Spin-1 Heisenberg Antiferromagnetic Chain after a Quantum Quench of the Uniaxial Anisotropy

2016

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In the framework of the matrix product state representation the effect of a sudden turning on of the uniaxial anisotropy on the time evolution of the Haldane state has been investigated. Depending on the value of the uniaxial anisotropy parameter, the calculations were derived within (or outside) the region where the Haldane gap survives. An exact expression for the time evolution of the Loschmidt echo has been derived and, moreover, its collapse and revival behaviour was captured. In addition, the non-local order parameter of a time evolving state was tracked, revealing two types of relaxations.

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Thermodynamic Limit of Density Matrix Renormalization

Cited by 1,010 publications

References 17 publications

Non-universal equilibrium crystal shape results from sticky steps

Non-universal equilibrium crystal shape results from sticky steps

Renormalization algorithm for the calculation of spectra of interacting quantum systems

Relaxation Dynamics in the Spin-1 Heisenberg Antiferromagnetic Chain after a Quantum Quench of the Uniaxial Anisotropy

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