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Register a new userTBA and TCSA with boundaries and excited states
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We study the spectrum of the scaling Lee-Yang model on a finite interval from two points of view: via a generalisation of the truncated conformal space approach to systems with boundaries, and via the boundary thermodynamic Bethe ansatz. This allows reflection factors to be matched with specific boundary conditions, and leads us to propose a new (and non-minimal) family of reflection factors to describe the one relevant boundary perturbation in the model. The equations proposed previously for the ground state on an interval must be revised in certain regimes, and we find the necessary modifications by analytic continuation. We also propose new equations to describe excited states, and check all equations against boundary truncated conformal space data. Access to the finite-size spectrum enables us to observe boundary flows when the bulk remains massless, and the formation of boundary bound states when the bulk is massive.
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We propose an alternative, statistical, derivation of the Thermodynamic Bethe Ansatz based on the tree expansion of the Gaudin determinant. We illustrate the method on the simplest example of a theory with diagonal scattering and no bound states. We reproduce the expression for the free energy density and the finite size corrections to the energy of an excited state as well as the LeClair-Mussardo series for the one-point function for local operators.
TBA integral equations are proposed for 1-particle states in the sausage- and SS-models and their $sigma$-model limits. Combined with the ground state TBA equations the exact mass gap is computed in the O(3) and O(4) nonlinear $sigma$-model and the results are compared to 3-loop perturbation theory and Monte Carlo data.
By considering the continuum scaling limit of the $A_{4}$ RSOS lattice model of Andrews-Baxter-Forrester with integrable boundaries, we derive excited state TBA equations describing the boundary flows of the tricritical Ising model. Fixing the bulk weights to their critical values, the integrable boundary weights admit a parameter $xi $ which plays the role of the perturbing boundary field $phi_{1,3}$ and induces the renormalization group flow between boundary fixed points. The boundary TBA equations determining the RG flows are derived in the $mathcal{B}_{(1,2)}to mathcal{B}_{(2,1)}$ example. The induced map between distinct Virasoro characters of the theory are specified in terms of distribution of zeros of the double row transfer matrix.
We argue that the entanglement entropy for a very small subsystem obeys a property which is analogous to the first law of thermodynamics when we excite the system. In relativistic setups, its effective temperature is proportional to the inverse of the subsystem size. This provides a universal relationship between the energy and the amount of quantum information. We derive the results using holography and confirm them in two dimensional field theories. We will also comment on an example with negative specific heat and suggest a connection between the second law of thermodynamics and the strong subadditivity of entanglement entropy.
In the ferromagnetic phase of the q-state Potts model, switching on an external magnetic field induces confinement of the domain wall excitations. For the Ising model (q = 2) the spectrum consists of kink-antikink states which are the analogues of mesonic states in QCD, while for q = 3, depending on the sign of the field, the spectrum may also contain three-kink bound states which are the analogues of the baryons. In recent years the resulting hadron spectrum was described using several different approaches, such as quantum mechanics in the confining linear potential, WKB methods and also the Bethe-Salpeter equation. Here we compare the available predictions to numerical results from renormalization group improved truncated conformal space approach (RG-TCSA). While mesonic states in the Ising model have already been considered in a different truncated Hamiltonian approach, this is the first time that a precision numerical study is performed for the 3-state Potts model. We find that the semiclassical approach provides a very accurate description for the mesonic spectrum in all the parameter regime for weak magnetic field, while the low-energy expansion from the Bethe-Salpeter equation is only valid for very weak fields where it gives a slight improvement over the semiclassical results. In addition, we confirm the validity of the recent predictions for the baryon spectrum obtained from solving the quantum mechanical three-body problem.
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