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 revisit the phase diagram of the dimerized XXZ spin-
21 chain with nearest-neighbor couplings which was studied numerically in Phys. Rev. B 106, L201106 (2022). The model has isotropic
XY couplings which have a uniform value and
ZZ couplings which have a dimerized form, with strengths
Ja and
Jb on alternate bonds. We find a rich phase diagram in the region of positive
Ja, Jb. We provide a detailed understanding of the different phases and associated quantum phase transitions using a combination of mean-field theory, low-energy effective Hamiltonians, renormalization group calculations employing the technique of bosonization, and numerical calculations using the density-matrix renormalization group (DMRG) method. The phase diagram consists of two Ising paramagnetic phases called IPM
0 and IPM
π, and a phase with Ising Neel order called IN; all these phases are gapped. The phases IPM
0 and IPM
π are separated by a gapless phase transition line given by
0≤Ja=Jb≤1 which is described by a conformal field theory with central charge
c=1. There are two gapless phase transition lines separating IPM
0 from IN and IPM
π from IN; these are described by conformal field theories with
c=21 corresponding to quantum Ising transitions. The
c=1 line bifurcates into the two
c=21 lines at the point
Ja=Jb=1; the shape of the bifurcation is found analytically using RG calculations. A symmetry analysis shows that IPM
0 is a topologically trivial phase while IPM
π is a time-reversal symmetry-protected topological phase (SPT) with spin-
21 states at the two ends of an open system. The numerical results obtained by the DMRG method are in good agreement with the analytical results. Finally we propose experimental platforms for testing our results.
We study the ground state quantum phase transition by means of entanglement in the one-dimensional asymmetric Hubbard model with open boundary conditions. The local entanglement between the middle two sites and the rest of the system, and the block entanglement between the left and right portions of the system, are calculated using the density-matrix renormalization group (DMRG) method. We find that the entanglement shows interesting scaling and singular behavior around the phase transition line.
Recently, it has been proposed that higher-spin analogs of the Kitaev interactions
K>0 may also occur in a number of materials with strong Hund's and spin-orbit coupling. In this work, we use Lanczos diagonalization and density matrix renormalization group methods to investigate numerically the
S=1 Kitaev-Heisenberg model. The ground-state phase diagram and quantum phase transitions are investigated by employing local and nonlocal spin correlations. We identify two ordered phases at negative Heisenberg coupling
J<0: a ferromagnetic phase with $\ensuremath{\langle}{S}_{i}^{z}{S}_{i+1}^{z}\ensuremath{\rangle}>0$ and an intermediate left-left-right-right phase with $\ensuremath{\langle}{S}_{i}^{x}{S}_{i+1}^{x}\ensuremath{\rangle}\ensuremath{\ne}0$. A quantum spin liquid is stable near the Kitaev limit, while a topological Haldane phase is found for
J>0.
In this paper, starting from a lattice model of topological insulators, we study the quantum phase transitions among different quantum states, including quantum spin Hall state, quantum anomalous Hall state and normal band insulator state by calculating their topological properties (edge states, quantized spin Hall conductivities and the number of zero mode on a Pi-flux). We find that there exist universal features for the topological quantum phase transitions (TQPTs) in different cases : the emergence of nodal fermions at high symmetry points, the non-analytic third derivative of ground state energy and the jumps of the topological "order parameters". In particular, the relation between TQPTs and symmetries of the systems are explored : different TQPTs are protected by different (global) symmetries and then described by different topological "order parameters".
We revisit the phase diagram of the dimerized XXZ spin-
21 chain with nearest-neighbor couplings which was studied numerically by Mondal et al. [Phys. Rev. B 106, L201106 (2022)]. The model has isotropic
XY couplings which have a uniform value and
ZZ couplings which have a dimerized form, with strengths
Ja and
Jb on alternate bonds. We find a rich phase diagram in the region of positive
Ja,Jb. We provide a detailed understanding of the different phases and associated quantum phase transitions using a combination of mean-field theory, low-energy effective Hamiltonians, renormalization group calculations employing the technique of bosonization, and numerical calculations using the density-matrix renormalization group (DMRG) method. The phase diagram consists of two Ising paramagnetic phases called
IPM0 and ${\mathrm{IPM}}_{\ensuremath{\pi}}$, and a phase with Ising Neel (IN) order; all these phases are gapped. The phases
IPM0 and ${\mathrm{IPM}}_{\ensuremath{\pi}}$ are separated by a gapless phase transition line $0\ensuremath{\le}{J}_{a}={J}_{b}\ensuremath{\le}1$---the well-known Tomonaga Luttinger liquid captured by a conformal field theory (CFT) with central charge
c=1. In contrast, there are two phase transition lines separating
IPM0 or the ${\mathrm{IPM}}_{\ensuremath{\pi}}$ from IN that are described by
c=21 CFTs and correspond to quantum Ising transitions. In fact, the
c=1 line bifurcates into the two
c=21 lines at the point
Ja=Jb=1; the shape of the bifurcation is found analytically using RG calculations. A symmetry analysis shows that
IPM0 is a topologically trivial phase while ${\mathrm{IPM}}_{\ensuremath{\pi}}$ is a time-reversal symmetry-protected topological phase (SPT) with spin-
21 states at the two ends of an open system. A gap opens in the low-energy spectrum whenever one moves away from one of the phase transition lines; the scaling of the gap with the distance from a transition line is found analytically using the RG method. The numerical results obtained by the DMRG method are in good agreement with the analytical results. Further, we show that useful insights into the nature of the phase diagram of the above Hamiltonian, particularly the SPT as well as the phase transitions, is obtained via Kramers-Wannier duality to a deformed quantum Ashkin-Teller model. Finally, we propose experimental platforms for testing our results.