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A<sc>bstract</sc> For the class of 1 + 1 dimensional field theories referred to as the non-linear sigma models, there is known to be a deep connection between classical integrability and one-loop renormalizability. In this work, the phenomenon is reviewed on the example of the so-called fully anisotropic SU(2) Principal Chiral Field (PCF). Along the way, we discover a new classically integrable four parameter family of sigma models, which is obtained from the fully anisotropic SU(2) PCF by means of the Poisson-Lie deformation. The theory turns out to be one-loop renormalizable and the system of ODEs describing the flow of the four couplings is derived. Also provided are explicit analytical expressions for the full set of functionally independent first integrals (renormalization group invariants). 

Abstract Confinement of topological excitations into particle-like states - typically associated with theories of elementary particles - are known to occur in condensed matter systems, arising as domain-wall confinement in quantum spin chains. However, investigation of confinement in the condensed matter setting has rarely ventured beyond lattice spin systems. Here we analyze the confinement of sine-Gordon solitons into mesonic bound states in a perturbed quantum sine-Gordon model. The latter describes the scaling limit of a one-dimensional, quantum electronic circuit (QEC) array, constructed using experimentally-demonstrated QEC elements. The scaling limit is reached faster for the QEC array compared to spin chains, allowing investigation of the strong-coupling regime of this model. We compute the string tension of confinement of sine-Gordon solitons and the changes in the low-lying energy spectrum. These results, obtained using the density matrix renormalization group method, could be verified in a quench experiment using state-of-the-art QEC technologies. 

The entanglement spectra for a subsystem in a spin chain fine-tuned to a quantum-critical point contains signatures of the underlying quantum field theory that governs its low-energy properties. For an open chain with given boundary conditions described by a two-dimensional (2D) conformal field theory (CFT), the entanglement spectrum of the left/right half of the system coincides with a boundary CFT spectrum, where one of the boundary conditions arise due to the “entanglement cut.” The latter has been argued to be conformal and has been numerically found to be the “free” boundary condition for Ising, Potts, and free boson theories. For these models, the free boundary condition for the lattice degree of freedom has a counterpart in the continuum theory. However, this is not true in general. Here, this question is analyzed for the unitary minimal models of 2D CFTs using the density matrix renormalization group technique. The entanglement spectra are computed for blocks of spins in open chains of A-type restricted solid-on-solid models with identical boundary conditions at the ends. The imposed boundary conditions are realized exactly for these lattice models due to their integrable nature. The obtained entanglement spectra are in good agreement with certain boundary CFT spectra. The boundary condition for the entanglement cut is found to be conformal and to coincide with the one with the highest boundary entropy. This identification enables determination of the exponents governing the unusual corrections to the entanglement entropy from the CFT partition functions. These are compared with numerical results. 

It is known that for the Heisenberg XXZ spin - chain in the critical regime, the scaling limit of the vacuum Bethe roots yields an infinite set of numbers that coincide with the energy spectrum of the quantum mechanical 3D anharmonic oscillator. The discovery of this curious relation, among others, gave rise to the approach referred to as the ODE/IQFT (or ODE/IM) correspondence. Here we consider a multiparametric generalization of the Heisenberg spin chain, which is associated with the inhomogeneous six-vertex model. When quasi-periodic boundary conditions are imposed the lattice system may be explored within the Bethe Ansatz technique. We argue that for the critical spin chain, with a properly formulated scaling limit, the scaled Bethe roots for the ground state are described by second order differential equations, which are multi-parametric generalizations of the Schrödinger equation for the anharmonic oscillator.