Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userMomentum-Space Entanglement in Heisenberg Spin-Half Ladders
238
0
0.0
(
0
)
Authors
Rex Lundgren
Ask ChatGPT about the research
No Arabic abstract
We analytically study momentum-space entanglement in quantum spin-half ladders consisting of two coupled critical XXZ spin-half chains using field theoretical methods. When the system is gapped, the momentum-space entanglement Hamiltonian is described by a conformal field theory with a central charge of two. This is in contrast to entanglement Hamiltonians of various real-space partitions of gapped-spin ladders that have a central charge of one. When the system is gapless, we interestingly find that the entanglement Hamiltonian consist of one gapless mode linear in subsystem momentum and one mode with a flat dispersion relation. We also find that the momentum-space entanglement entropy obeys a volume law.
rate research
Read More
We examine the entanglement properties of the spin-half Heisenberg model on the two-dimensional square-lattice bilayer based on quantum Monte Carlo calculations of the second Renyi entanglement entropy. In particular, we extract the dominant area-law contribution to the bipartite entanglement entropy that shows a non-monotonous behavior upon increasing the inter-layer exchange interaction: a local maximum in the area-law coefficient is located at the quantum critical point separating the antiferromagnetically ordered region from the disordered dimer-singlet regime. Furthermore, we consider subleading logarithmic corrections to the Renyi entanglement entropy scaling. Employing different subregion shapes, we isolate the logarithmic corner term from the logarithmic contribution due to Goldstone modes that is found to be enhanced in the limit of decoupled layers. At the quantum critical point, we estimate a contribution of $0.016(1)$ due to each $90^{circ}$ corner. This corner term at the SU(2) quantum critical point deviates from the Gaussian theory value, while it compares well with recent numerical linked cluster calculations on the bilayer model.
The study of randomness in low-dimensional quantum antiferromagnets is at the forefront of research in the field of strongly correlated electron systems, yet there have been relatively few experimental model systems. Complementary neutron scattering and numerical experiments demonstrate that the spin-diluted Heisenberg antiferromagnet La2Cu(1-z)(Zn,Mg)zO4 is an excellent model material for square-lattice site percolation in the extreme quantum limit of spin one-half. Measurements of the ordered moment and spin correlations provide important quantitative information for tests of theories for this complex quantum-impurity problem.
We analyze the possible existence of topological phases in two-legged spin ladders considering a staggered interaction in both chains. When the staggered interaction in one chain is shifted by one site with respect to the other chain, the model can be mapped, in the continuum limit, into a non linear sigma model NL$sigma$M plus a topological term which is nonvanishing when the number of legs is two. This implies the existence of a critical point which distinguishes two phases. We perform a numerical analysis of energy levels, parity and string non-local order parameters, correlation functions between $x,y,z$ components of spins at the edges of an open ladder, the degeneracy of the entanglement spectrum and the entanglement entropy in order to characterize these two different phases. Finally, we identify one phase with a Mott insulator and the other one with a Haldane insulator.
We report a novel crossover behavior in the long-range-ordered phase of a prototypical spin-$1/2$ Heisenberg antiferromagnetic ladder compound $mathrm{(C_7H_{10}N)_2CuBr_4}$. The staggered order was previously evidenced from a continuous and symmetric splitting of $^{14}$N NMR spectral lines on lowering temperature below $T_csimeq 330$ mK, with a saturation towards $simeq 150$ mK. Unexpectedly, the split lines begin to further separate away below $T^*sim 100$ mK while the line width and shape remain completely invariable. This crossover behavior is further corroborated by the NMR relaxation rate $T_1^{-1}$ measurements. A very strong suppression reflecting the ordering, $T_1^{-1}sim T^{5.5}$, observed above $T^*$, is replaced by $T_1^{-1}sim T$ below $T^*$. These original NMR features are indicative of unconventional nature of the crossover, which may arise from a unique arrangement of the ladders into a spatially anisotropic and frustrated coupling network.
We study the momentum space entanglement spectra of bosonic and fermionic formulations of the spin-1/2 XXZ chain with analytical methods and exact diagonalization. We investigate the behavior of the entanglement gaps, present in both partitions, across quantum phase transitions in the XXZ chain. In both cases, finite size scaling reveals that the entanglement gap closure does not occur at the physical transition points. For bosons, we find that the entanglement gap observed in [Thomale et al., Phys. Rev. Lett. 105, 116805 (2010)] depends on the scaling dimension of the conformal field theory as varied by the XXZ anisotropy. For fermions, the infinite entanglement gap present at the XX point persists well past the phase transition at the Heisenberg point. We elaborate on how these shifted transition points in the entanglement spectra may in fact support the numerical study of physical transitions in the momentum space density matrix renormalization group.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
