Related papers: Singularity with and without disorder at AKLT poin…
Solvable matrix product and projected entangled pair states evolved by dual and ternary-unitary quantum circuits have analytically accessible correlation functions. Here, we investigate the influence of disorder. Specifically, we compute…
We discuss the relation between singularities of correlation functions and causal properties of the bulk spacetime in the context of the AdS/CFT correspondence. In particular, we argue that the boundary field theory correlation functions…
Strange correlators are useful tools for diagnosing symmetry-protected topological states from their bulk wave functions. We study strange correlators for one-dimensional fermionic symmetry-protected topological states using fixed-point…
The spatial structure of wave functions of anomalously localized states (ALS) in disordered conductors is studied in the framework of the $\sigma$--model approach. These states are responsible for slowly decaying tails of various…
We reconsider the random bond antiferromagnetic spin-1/2 chain for weak disorder and demonstrate the existence of crossover length scale x_W that diverges with decreasing strength of the disorder. Recent DMRG calculations [Phys. Rev. Lett.…
We consider localisation problems belonging to the chiral symmetry classes, in which sublattice symmetry is responsible for singular behaviour at a band centre. We formulate models which have the relevant symmetries and which are…
We solve the nonlinear Dirichlet problem (uniquely) for functions with prescribed asymptotic singularities at a finite number of points, and with arbitrary continuous boundary data, on a domain in euclidean space. The main results apply, in…
The all-orders beta function is used to study disordered Dirac fermions in 2D. The generic strong coupling fixed `points' of anisotropic current-current interactions at large distances are actually isotropic manifolds corresponding to…
In systems displaying a bulk first-order transition the order parameter may vanish continuously at a free surface, a phenomenon which is called surface-induced disorder. In the presence of surface-induced disorder the correlation lengths,…
Commensurate-incommensurate change on the one-dimensional S=1 bilinear-biquadratic model (${\cal H}(\alpha)=\sum_i \{{\bf S}_i\cdot {\bf S}_{i+1} +\alpha ({\bf S}_i\cdot{\bf S}_{i+1})^2\}$) is examined. The gapped Haldane phase has two…
The n-particle periodic Toda chain is a well known example of an integrable but nonseparable Hamiltonian system in R^{2n}. We show that Sigma_k, the k-fold singularities of the Toda chain, ie points where there exist k independent linear…
Nonlinear sigma models with non-compact target space and non-amen-able symmetry group were introduced long ago in the study of disordered electron systems. They also occur in dimensionally reduced quantum gravity; recently they have been…
We study singularity formation in nonlinear differential equations of order $m\leqslant 2$, $y^{(m)}=A(x^{-1},y)$. We assume $A$ is analytic at $(0,0)$ and $\partial_y A(0,0)=\lambda\ne 0$ (say, $\lambda=(-1)^m$). If $m=1$ we assume…
We study entanglement in Valence-Bond-Solid state. It describes the ground state of Affleck, Kennedy, Lieb and Tasaki quantum spin chain. The AKLT model has a gap and open boundary conditions. We calculate an entropy of a subsystem…
We investigate the nature of the superfluid-insulator quantum phase transition driven by disorder for non-interacting ultracold atoms on one-dimensional lattices. We consider two different cases: Anderson-type disorder, with local energies…
This work offers a new prospective on asymptotic perturbation theory for varying self-adjoint extensions of symmetric operators. Employing symplectic formulation of self-adjointness we obtain a new version of Krein formula for resolvent…
We identify subsystem fluctuations (variances) that measure entanglement in an arbitrary bipartite pure state. These fluctuations are of observables that generalize the notion of polarization to an arbitrary N-level subsystem. We express…
Lieb-Schultz-Mattis (LSM) anomalies are powerful symmetry-based constraints on the correlation, entanglement and dynamics of quantum many-body systems. In this review, we discuss various LSM anomalies and anomaly matching. We start with a…
The AKLT spin chain is the prototypical example of a frustration-free quantum spin system with a spectral gap above its ground state. Affleck, Kennedy, Lieb, and Tasaki also conjectured that the two-dimensional version of their model on the…
We study the Anderson single-level quantum dot attached to two BCS superconducting leads with the same gap size. We reveal that a system with asymmetric tunnel coupling to the leads ($\Gamma_{L}\neq\Gamma_{R}$) can be related to the…