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• W2149075194 abstract "We present a matrix product state (MPS) algorithm to approximate ground states of translationally invariant systems with periodic boundary conditions. For a fixed value of the bond dimension $D$ of the MPS, we discuss how to minimize the computational cost to obtain a seemingly optimal MPS approximation to the ground state. In a chain with $N$ sites and correlation length $ensuremath{xi}$, the computational cost formally scales as $g(D,ensuremath{xi}/N){D}^{3}$, where $g(D,ensuremath{xi}/N)$ is a nontrivial function. For $ensuremath{xi}ensuremath{ll}N$, this scaling reduces to ${D}^{3}$, independent of the system size $N$, making our method $N$ times faster than previous proposals. We apply the algorithm to obtain MPS approximations for the ground states of the critical quantum Ising and Heisenberg spin-$1/2$ models as well as for the noncritical Heisenberg spin-$1$ model. In the critical case, for any chain length $N$, we find a model-dependent bond dimension $D(N)$ above which the polynomial decay of correlations is faithfully reproduced throughout the entire system." @default.
• W2149075194 created "2016-06-24" @default.
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• W2149075194 date "2011-03-17" @default.
• W2149075194 modified "2023-09-27" @default.
• W2149075194 title "Exploiting translational invariance in matrix product state simulations of spin chains with periodic boundary conditions" @default.
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• W2149075194 doi "https://doi.org/10.1103/physrevb.83.125104" @default.
• W2149075194 hasPublicationYear "2011" @default.
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