Stiffness in 1D Matrix Product States with periodic boundary conditions

Abstract

We discuss in details a modified variational matrix-product-state algorithm for periodic boundary conditions, based on a recent work by P. Pippan, S.R. White and H.G. Everts, Phys. Rev. B 81, 081103(R) (2010), which enables one to study large systems on a ring (composed of N ~ 10^2 sites). In particular, we introduce a couple of improvements that allow to enhance the algorithm in terms of stability and reliability. We employ such method to compute the stiffness of one-dimensional strongly correlated quantum lattice systems. The accuracy of our calculations is tested in the exactly solvable spin-1/2 Heisenberg chain.

23 pages, 9 figures. Published version, extensive changes

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• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• The density-matrix renormalization group in the age of matrix product states
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• DMRG and periodic boundary conditions: a quantum information perspective
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• Stiffness in 1D Matrix Product States with periodic boundary conditions
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Cited by in corpus (13)

• Matrix product states for critical spin chains: finite size scaling versus finite entanglement scaling
• Preformed pairs in flat Bloch bands
• Out of equilibrium dynamics with Matrix Product States
• Optimal Persistent Currents for Interacting Bosons on a Ring with a Gauge Field
• Efficient MPS methods for extracting spectral information on rings and cylinders
• Topological pumping in the one-dimensional Bose-Hubbard model
• An Efficient Density Matrix Renormalization Group Algorithm for Chains with Periodic Boundary Condition
• Stiffness in 1D Matrix Product States with periodic boundary conditions
• Phase-induced transport in atomic gases: from superfluid to Mott insulator
• Symmetries and entanglement in the one-dimensional spin-1/2 XXZ model
• Geometric entanglement from matrix product state representations
• Topological Defects in Quantum Field Theory with Matrix Product States
• Finite-size scaling on the torus with periodic projected entangled-pair states