We have developed an efficient tensor network algorithm for spin ladders, which generates ground-state wave functions for infinite-size quantum spin ladders. The algorithm is able to efficiently compute the ground-state fidelity per lattice site, a universal phase transition marker, thus offering a powerful tool to unveil quantum many-body physics underlying spin ladders. To illustrate our scheme, we consider the two-leg and three-leg Heisenberg spin ladders with staggering dimerization. The ground-state phase diagram thus yielded is reliable, compared with the previous studies based on the density matrix renormalization group. Our results indicate that the ground-state fidelity per lattice site successfully captures quantum criticalities in spin ladders. 71.10.Fd Introduction. Tensor networks (TN) provide a convenient means to represent quantum wave functions in classical simulations of quantum many-body lattice systems, such as the matrix product states (MPS) [1][2][3][4][5] in one spatial dimension and the projected entangled-pair state (PEPS) [6][7][8] in two and higher spatial dimensions. The development of various numerical algorithms in the context of the TN representations has led to significant advances in our understanding of quantum many-body lattice systems in both one and two spatial dimensions [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Lying between quantum lattice systems in one and two spatial dimensions, spin ladders have attracted a lot of attention, due to their intriguing critical properties. Given the importance of spin ladder systems in condensed matter physics, it is somewhat surprising that no efforts have been made to develop any efficient algorithm in the context of the TN representations.This paper aims to fill in this gap. The algorithm generates efficiently ground-state wave functions for infinite-size spin ladders. In addition, it allows to efficiently compute the ground-state fidelity per lattice site, a universal phase transition marker, thus offering a powerful tool to unveil quantum many-body physics underlying spin ladders. In fact, as argued in Refs. [18][19][20][21][22][23], the ground-state fidelity per lattice site is able to capture drastic changes of the ground-state wave functions around a critical point. To illustrate our scheme, we consider the two-leg and three-leg Heisenberg spin ladders with staggering dimerization. The ground-state phase diagram thus yielded is reliable, compared with the previous studies [24,25] based on the density matrix renormalization group (DMRG) [26]. Our results indicate that the ground-state fidelity per lattice site successfully captures quantum criticalities in spin ladders.Tensor network representation for spin ladders. Let us describe the TN representation suitable to describe a groundstate wave function for an infinite-size spin ladder. Suppose the Hamiltonian is translationally invariant under shifts by either one or two lattice sites along the legs: H = i,α h i,α , with the i, α -th plaquette Hamiltonian density h i,α...

The ground-state fidelity per lattice site is computed for the quantum threestate Potts model in a transverse magnetic field on an infinite-size lattice in one spatial dimension in terms of the infinite matrix product state algorithm. It is found that, on the one hand, a pinch point is identified on the fidelity surface around the critical point, and on the other hand, the ground-state fidelity per lattice site exhibits bifurcations at pseudo critical points for different values of the truncation dimension, which in turn approach the critical point as the truncation dimension becomes large. This implies that the ground-state fidelity per lattice site enables us to capture spontaneous symmetry breaking when the control parameter crosses the critical value. In addition, a finite-entanglement scaling of the von Neumann entropy is performed with respect to the truncation dimension, resulting in a precise determination of the central charge at the critical point. Finally, we compute the transverse magnetization, from which the critical exponent β is extracted from the numerical data.

We numerically investigate the two-dimensional q-state quantum Potts model on the infinite square lattice by using the infinite projected entangled-pair state (iPEPS) algorithm. We show that the quantum fidelity, defined as an overlap measurement between an arbitrary reference state and the iPEPS groundstate of the system, can detect q-fold degenerate groundstates for the Z q broken-symmetry phase. Accordingly, a multiple-bifurcation of the quantum groundstate fidelity is shown to occur as the transverse magnetic field varies from the symmetry phase to the broken-symmetry phase, which means that a multiple-bifurcation point corresponds to a critical point. A (dis-)continuous behavior of quantum fidelity at phase transition points characterizes a (dis-)continuous phase transition. Similar to the characteristic behavior of the quantum fidelity, the magnetizations, as order parameters, obtained from the degenerate groundstates exhibit multiple bifurcation at critical points. Each order parameter is also explicitly demonstrated to transform under the subgroup of the Z q symmetry group. We find that the q-state quantum Potts model on the square lattice undergoes a discontinuous (first-order) phase transition for q = 3 and q = 4, and a continuous phase transition for q = 2 (the 2D quantum transverse Ising model).

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The von Neumann entanglement entropy is used to estimate the critical point h c /J ≃ 0.143(3) of the mixed ferro-antiferromagnetic three-state quantum Potts model, where X i and R i are standard three-state Potts spin operators and J > 0 is the antiferromagnetic coupling parameter. This critical point value gives improved estimates for two Kosterlitz-Thouless transition points in the antiferromagnetic (β < 0) region of the ∆-β phase diagram of the three-state quantum chiral clock model, where ∆ and β are, respectively, the chirality and coupling parameters in the clock model. These are the transition points β c ≃ −0.143(3) at ∆ = 1 2 between incommensurate and commensurate phases and β c ≃ −7.0(1) at ∆ = 0 between disordered and incommensurate phases. The von Neumann entropy is also used to calculate the central charge c of the underlying conformal field theory in the massless phase h ≤ h c . The estimate c ≃ 1 in this phase is consistent with the known exact value at the particular point h/J = −1 corresponding to the purely antiferromagnetic three-state quantum Potts model. The algebraic decay of the Potts spin-spin correlation in the massless phase is used to estimate the continuously varying critical exponent η.