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Register a new userEntanglement entropy scaling in the bilayer Heisenberg spin system
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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.
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The scaling of entanglement entropy for the nearest neighbor antiferromagnetic Heisenberg spin model is studied computationally for clusters joined by a single bond. Bisecting the balanced three legged Bethe Cluster, gives a second Renyi entropy and the valence bond entropy which scales as the number of sites in the cluster. For the analogous situation with square clusters, i.e. two $L times L$ clusters joined by a single bond, numerical results suggest that the second Renyi entropy and the valence bond entropy scales as $L$. For both systems, the environment and the system are connected by the single bond and interaction is short range. The entropy is not constant with system size as suggested by the area law.
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.
We develop a nonequilibrium increment method to compute the Renyi entanglement entropy and investigate its scaling behavior at the deconfined critical (DQC) point via large-scale quantum Monte Carlo simulations. To benchmark the method, we first show that at an conformally-invariant critical point of O(3) transition, the entanglement entropy exhibits universal scaling behavior of area law with logarithmic corner corrections and the obtained correction exponent represents the current central charge of the critical theory. Then we move on to the deconfined quantum critical point, where although we still observe similar scaling behavior but with a very different exponent. Namely, the corner correction exponent is found to be negative. Such a negative exponent is in sharp contrast with positivity condition of the Renyi entanglement entropy, which holds for unitary conformal field theories. Our results unambiguously reveal fundamental differences between DQC and QCPs described by unitary CFTs.
The scaling of entanglement entropy is computationally studied in several $1le d le 2$ dimensional free fermion systems that are connected by one or more point contacts (PC). For both the $k$-leg Bethe lattice $(d =1)$ and $d=2$ rectangular lattices with a subsystem of $L^d$ sites, the entanglement entropy associated with a {sl single} PC is found to be generically $S sim L$. We argue that the $O(L)$ entropy is an expression of the subdominant $O(L)$ entropy of the bulk entropy-area law. For $d=2$ (square) lattices connected by $m$ PCs, the area law is found to be $S sim aL^{d-1} + b m log{L}$ and is thus consistent with the anomalous area law for free fermions ($S sim L log{L}$) as $m rightarrow L$. For the Bethe lattice, the relevance of this result to Density Matrix Renormalization Group (DMRG) schemes for interacting fermions is discussed.
We explore several classes of quadrupolar ordering in a system of antiferromagnetically coupled quantum spin-1 dimers, which are stacked in the triangular lattice geometry forming a bilayer. Low-energy properties of this model is described by an $mathcal{S}=1$ hard-core bosonic degrees of freedom defined on each dimer-bond, where the singlet and triplet states of the dimerized spins are interpreted as the vacuum and the occupancy of boson, respectively. The number of bosons per dimer and the magnetic and density fluctuations of bosons are controlled by the inter-dimer Heisenberg interactions. In a solid phase where each dimer hosts one boson and the inter-dimer interaction is weak, a conventional spin nematic phase is realized by the pair-fluctuation of bosons. Larger inter-dimer interaction favors Bose Einstein condensates (BEC) carrying quadrupolar moments. Among them, we find one exotic phase where the quadrupoles develop a spatially modulated structure on the top of a uniform BEC, interpreted in the original dimerized spin-1 model as coexistent $p$-type nematic and 120$^circ$-magnetic correlations. This may explain an intriguing nonmagnetic phase found in Ba$_{3}$ZnRu$_{2}$O$_{9}$.
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