Renormalization algorithm for the calculation of spectra of interacting quantum systems

Abstract

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. Its virtues are shown in the study of bilinear--biquadratic S=1 chains.

arXiv commentCorrected version. We have added an appendix with an extended explanation of the implementation of our algorithm

References in corpus (11)

• Entanglement in quantum critical phenomena
• Efficient simulation of one-dimensional quantum many-body systems
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• DMRG and periodic boundary conditions: a quantum information perspective
• Spin-exchange interactions of spin-one bosons in optical lattices: singlet, nematic and dimerized Phases
• Implementation of Spin Hamiltonians in Optical Lattices
• Phase diagram of spin-1 bosons on one-dimensional lattices
• Search for the Nondimerized Quantum Nematic Phase in the Spin-1 Chain
• Probable absence of a quadrupolar spin-nematic phase in the bilinear-biquadratic spin-1 chain
• Unveiling Order behind Complexity: Coexistence of Ferromagnetism and Bose-Einstein Condensation

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