Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSpin-Peierls transition of the dimer phase of the $J_1-J_2$ model: Energy cusp and CuGeO$_3$ thermodynamics
107
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The spin-Peierls transition is modeled in the dimer phase of the spin-$1/2$ chain with exchanges $J_1$, $J_2 = alpha J_1$ between first and second neighbors. The degenerate ground state generates an energy cusp that qualitatively changes the dimerization $delta(T)$ compared to Peierls systems with nondegenerate ground states. The parameters $J_1 = 160$ K, $alpha = 0.35$ plus a lattice stiffness account for the magnetic susceptibility of CuGeO$_3$, its specific heat anomaly, and the $T$ dependence of the lowest gap.
rate research
Read More
The spin-Peierls transition at $T_{SP}$ of spin-$1/2$ chains with isotropic exchange interactions has previously been modeled as correlated for $T > T_{SP}$ and mean field for $T < T_{SP}$. We use correlated states throughout in the $J_1-J_2$ model with antiferromagnetic exchange $J_1$ and $J_2 = alpha J_1$ between first and second neighbors, respectively, and variable frustration $0 leq alpha leq 0.50$. The thermodynamic limit is reached at high $T$ by exact diagonalization of short chains and at low $T$ by density matrix renormalization group calculations of progressively longer chains. In contrast to mean field results, correlated states of 1D models with linear spin-phonon coupling and a harmonic adiabatic lattice provide an internally consistent description in which the parameter $T_{SP}$ yields both the stiffness and the lattice dimerization $delta(T)$. The relation between $T_{SP}$ and $Delta(delta,alpha)$, the $T = 0$ gap induced by dimerization, depends strongly on $alpha$ and deviates from the BCS gap relation that holds in uncorrelated spin chains. Correlated states account quantitatively for the magnetic susceptibility of TTF-CuS$_4$C$_4$(CF$_3$)$_4$ crystals ($J_1 = 79$ K, $alpha = 0$, $T_{SP} = 12$ K) and CuGeO$_3$ crystals ($J_1 = 160$ K, $alpha = 0.35$, $T_{SP} = 14$ K). The same parameters describe the specific heat anomaly of CuGeO$_3$ and inelastic neutron scattering. Modeling the spin-Peierls transition with correlated states exploits the fact that $delta(0)$ limits the range of spin correlations at $T = 0$ while $T > 0$ limits the range at $delta= 0$.
The antiferromagnetic $J_1-J_2$ model is a spin-1/2 chain with isotropic exchange $J_1 > 0$ between first neighbors and $J_2 = alpha J_1$ between second neighbors. The model supports both gapless quantum phases with nondegenerate ground states and gapped phases with $Delta(alpha) > 0$ and doubly degenerate ground states. Exact thermodynamics is limited to $alpha = 0$, the linear Heisenberg antiferromagnet (HAF). Exact diagonalization of small systems at frustration $alpha$ followed by density matrix renormalization group (DMRG) calculations returns the entropy density $S(T,alpha,N)$ and magnetic susceptibility $chi(T,alpha,N)$ of progressively larger systems up to $N = 96$ or 152 spins. Convergence to the thermodynamics limit, $S(T,alpha)$ or $chi(T,alpha)$, is demonstrated down to $T/J sim 0.01$ in the sectors $alpha < 1$ and $alpha > 1$. $S(T,alpha)$ yields the critical points between gapless phases with $S^prime(0,alpha) > 0$ and gapped phases with $S^prime(0,alpha) = 0$. The $S^prime(T,alpha)$ maximum at $T^*(alpha)$ is obtained directly in chains with large $Delta(alpha)$ and by extrapolation for small gaps. A phenomenological approximation for $S(T,alpha)$ down to $T = 0$ indicates power-law deviations $T^{-gamma(alpha)}$ from $exp(-Delta(alpha)/T)$ with exponent $gamma(alpha)$ that increases with $alpha$. The $chi(T,alpha)$ analysis also yields power-law deviations, but with exponent $eta(alpha)$ that decreases with $alpha$. $S(T,alpha)$ and the spin density $rho(T,alpha) = 4Tchi(T,alpha)$ probe the thermal and magnetic fluctuations, respectively, of strongly correlated spin states. Gapless chains have constant $S(T,alpha)/rho(T,alpha)$ for $T < 0.10$. Remarkably, the ratio decreases (increases) with $T$ in chains with large (small) $Delta(alpha)$.
The one-dimensional spin-S $J_1-J_2$ XY model is studied within the bosonization approach. Around the two limits ($J_2/J_1 ll 1,J_2/J_1 gg 1$) where a field theoretical analysis can be derived, we discuss the phases as well as the different phase transitions that occur in the model. In particular, it is found that the chiral critical spin nematic phase, first discovered by Nersesyan et al. (Phys. Rev. Lett. {bf 81}, 910 (1998)) for $S=1/2$, exists in the general spin-S case. The nature of the effective field theory that describes the transition between this chiral critical phase and a chiral gapped phase is also determined.
Strongly correlated systems with geometric frustrations can host the emergent phases of matter with unconventional properties. Here, we study the spin $S = 1$ Heisenberg model on the honeycomb lattice with the antiferromagnetic first- ($J_1$) and second-neighbor ($J_2$) interactions ($0.0 leq J_2/J_1 leq 0.5$) by means of density matrix renormalization group (DMRG). In the parameter regime $J_2/J_1 lesssim 0.27$, the system sustains a N{e}el antiferromagnetic phase. At the large $J_2$ side $J_2/J_1 gtrsim 0.32$, a stripe antiferromagnetic phase is found. Between the two magnetic ordered phases $0.27 lesssim J_2/J_1 lesssim 0.32$, we find a textit{non-magnetic} intermediate region with a plaquette valence-bond order. Although our calculations are limited within $6$ unit-cell width on cylinder, we present evidence that this plaquette state could be a strong candidate for this non-magnetic region in the thermodynamic limit. We also briefly discuss the nature of the quantum phase transitions in the system. We gain further insight of the non-magnetic phases in the spin-$1$ system by comparing its phase diagram with the spin-$1/2$ system.
Using density-matrix renormalization-group calculations for infinite cylinders, we elucidate the properties of the spin-liquid phase of the spin-$frac{1}{2}$ $J_1$-$J_2$ Heisenberg model on the triangular lattice. We find four distinct ground-states characteristic of a non-chiral, $Z_2$ topologically ordered state with vison and spinon excitations. We shed light on the interplay of topological ordering and global symmetries in the model by detecting fractionalization of time-reversal and space-group dihedral symmetries in the anyonic sectors, which leads to coexistence of symmetry protected and intrinsic topological order. The anyonic sectors, and information on the particle statistics, can be characterized by degeneracy patterns and symmetries of the entanglement spectrum. We demonstrate the ground-states on finite-width cylinders are short-range correlated and gapped; however some features in the entanglement spectrum suggest that the system develops gapless spinon-like edge excitations in the large-width limit.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
