Finite-size scaling for correlations of quantum spin chains at criticality

R. Bischof, P. R. Crompton

The leading corrections to finite-size scaling relations for the correlation length and twist order parameter of three mixed-spin quantum spin chains for the critical feature that develops at ϑ = π, corresponding to a change in the topological realization of the ground states, are identified.

D. P. Landau

W. W. Cheng, Zhijun Zhang, Longyan Gong +1 more

B. Pirvu, Guifré Vidal, Frank Verstraete +1 more

We investigate the use of matrix product states (MPS) to approximate ground states of critical quantum spin chains with periodic boundary conditions (PBC). We identify two regimes in the $(N,D)$ parameter plane, where $N$ is the size of the spin chain and $D$ is the dimension of the MPS matrices. In the first regime, MPS can be used to perform finite size scaling (FSS). In the complementary regime, the MPS simulations show instead the clear signature of finite entanglement scaling (FES). In the thermodynamic limit (or large $N$ limit), only MPS in the FSS regime maintain a finite overlap with the exact ground state. This observation has implications on how to correctly perform FSS with MPS as well as on the performance of recent MPS algorithms for systems with PBC. It also gives clear evidence that critical models can actually be simulated very well with MPS by using the right scaling relations; in the appendixes, we give an alternative derivation of the result of Pollmann et al. [Phys. Rev. Lett. 102, 255701 (2009)] relating the bond dimension of the MPS to an effective correlation length.

Y.J. Kim, M. Greven, U.‐J. Wiese +1 more

Shan-Wen Tsai, John Bradley Marston

We present a simple method, combining the density-matrix renormalization-group algorithm with finite-size scaling, which permits the study of critical behavior in quantum spin chains. Spin moments and dimerization are induced by boundary conditions at the chain ends and these exhibit power-law decay at critical points. Results are presented for the spin-$1/2$ Heisenberg antiferromagnet; an analytic calculation shows that logarithmic corrections to scaling can sometimes be avoided. We also examine the spin-1 chain at the critical point separating the Haldane gap and dimerized phases. Exponents for the dimer-dimer and the spin-spin correlation functions are consistent with results obtained from bosonization.