Journal
PHYSICAL REVIEW B
Volume 83, Issue 12, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.83.125104
Keywords
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Funding
- FWF [W1210]
- FWF SFB
- ERC [QUERG]
- ARC [FF0668731, DP0878830]
- Austrian Science Fund (FWF) [W1210] Funding Source: Austrian Science Fund (FWF)
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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 xi, the computational cost formally scales as g(D,xi/N)D-3, where g(D,xi/N) is a nontrivial function. For xi << 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.
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