We study the phase diagram of a one-dimensional version of the Kitaev spin-1/2 model with an extra "Γ term," using analytical, density matrix renormalization group and exact diagonalization methods. Two intriguing phases are found. In the gapless phase, although the exact symmetry group of the system is discrete, the low energy theory is described by an emergent SU(2)_{1} Wess-Zumino-Witten (WZW) model. On the other hand, the spin-spin correlation functions exhibit SU(2) breaking prefactors, even though the exponents and the logarithmic corrections are consistent with the SU(2)_{1} predictions. A modified non-Abelian bosonization formula is proposed to capture such exotic emergent "partial" SU(2) symmetry. In the ordered phase, there is numerical evidence for an O_{h}→D_{4} spontaneous symmetry breaking.
We analyze the antiferromagnetic
SU(3) Heisenberg chain by means of the density-matrix renormalization group. The results confirm that the model is critical and the computation of its central charge and the scaling dimensions of the first-excited states show that the underlying low-energy conformal field theory is the
SU(3)1 Wess-Zumino-Novikov-Witten model.
In this paper we study the ground-state properties of a ladder Hamiltonian with chiral
SU(2)-invariant spin interactions, a possible first step toward the construction of truly two-dimensional nontrivial systems with chiral properties starting from quasi-one-dimensional ones. Our analysis uses a recent implementation by us of
SU(2) symmetry in tensor network algorithms, specifically for infinite density matrix renormalization group. After a preliminary analysis with Kadanoff coarse graining and exact diagonalization for a small-size system, we discuss its bosonization and recap the continuum limit of the model to show that it corresponds to a conformal field theory, in agreement with our numerical findings. In particular, the scaling of the entanglement entropy as well as finite-entanglement scaling data show that the ground-state properties match those of the universality class of a
c=1 conformal field theory (CFT) in
(1+1) dimensions. We also study the algebraic decay of spin-spin and dimer-dimer correlation functions, as well as the algebraic convergence of the ground-state energy with the bond dimension, and the entanglement spectrum of half an infinite chain. Our results for the entanglement spectrum are remarkably similar to those of the spin-
21 Heisenberg chain, which we take as a strong indication that both systems are described by the same CFT at low energies, i.e., an
SU(2)1 Wess-Zumino-Witten theory. Moreover, we explain in detail how to construct matrix product operators for
SU(2)-invariant three-spin interactions, something that had not been addressed with sufficient depth in the literature.
We systematically study the phase diagram of
S=2 spin chain by means of density-matrix renormalization group and exact diagonalization. We confirm the presence of a dimer phase in the Affleck-Kennedy-Lieb-Tasaki (AKLT) and Scalapino-Zhang-Hanke (SZH) model and find that the whole phase boundary between dimer and SZH phases, including the multicritical point, is a critical line with central charge
c=5/2. Finally, we propose and confirm that this line corresponds to
SO(5)1 Wess-Zumino-Witten conformal field theory.
We investigate a phase transition in an SU(3) symmetric spin-1 chain. To study this transition, we numerically diagonalize an SU(3) symmetric Hamiltonian combining the Uimin-Lai-Sutherland (ULS) model Hamiltonian with the Hamiltonian of the exact trimer ground state (
Z3 symmetry breaking). Our numerical results are discussed on the basis of the conformal field theory (CFT) and the renormalization group (RG). We then show the phase transition between a trimer liquid phase (massless, no long-range order) and a trimer phase (spontaneously
Z3 symmetry breaking). Next, we find the central charge
c=2 in the massless phase, and
c<2 in the
Z3 symmetry broken phase. From these results, we identify the universality class of the critical trimer liquid phase, as well as the phase boundary between these two phases.
We present a study of the scaling behavior of the R\'enyi entanglement entropy (REE) in
SU(N) spin chain Hamiltonians, in which all of the spins transform under the fundamental representation. These
SU(N) spin chains are known to be quantum critical and described by a well known Wess-Zumino-Witten (WZW) nonlinear sigma model in the continuum limit. Numerical results from our lattice Hamiltonian are obtained using stochastic series expansion quantum Monte Carlo for both closed and open boundary conditions. As expected for this 1D critical system, the REE shows a logarithmic dependence on the subsystem size with a prefactor given by the central charge of the
SU(N) WZW model. We study in detail the subleading oscillatory terms in the REE under both periodic and open boundaries. Each oscillatory term is associated with a WZW field and decays as a power law with an exponent proportional to the scaling dimension of the corresponding field. We find that the use of periodic boundaries (where oscillations are less prominent) allows for a better estimate of the central charge, while using open boundaries allows for a better estimate of the scaling dimensions. We also present numerical data on the thermal R\'enyi entropy which equally allows for extraction of the central charge.