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Register a new userOverlaps after quantum quenches in the sine-Gordon model
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We present a numerical computation of overlaps in mass quenches in sine-Gordon quantum field theory using truncated conformal space approach (TCSA). To improve the cut-off dependence of the method, we use a novel running coupling definition which has a general applicability in free boson TCSA. The numerical results are used to confirm the validity of a previously proposed analytical Ansatz for the initial state in the sinh-Gordon quench.
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We study the quantum sine-Gordon model within a nonperturbative functional renormalization-group approach (FRG). This approach is benchmarked by comparing our findings for the soliton and lightest breather (soliton-antisoliton bound state) masses to exact results. We then examine the validity of the Lukyanov-Zamolodchikov conjecture for the expectation value $langle e^{frac{i}{2}nbetavarphi}rangle$ of the exponential fields in the massive phase ($n$ is integer and $2pi/beta$ denotes the periodicity of the potential in the sine-Gordon model). We find that the minimum of the relative and absolute disagreements between the FRG results and the conjecture is smaller than 0.01.
In this paper we study the $c$-function of the sine-Gordon model taking explicitly into account the periodicity of the interaction potential. The integration of the $c$-function along trajectories of the non-perturbative renormalization group flow gives access to the central charges of the model in the fixed points. The results at vanishing frequency $beta^2$, where the periodicity does not play a role, are retrieved and the independence on the cutoff regulator for small frequencies is discussed. Our findings show that the central charge obtained integrating the trajectories starting from the repulsive low-frequencies fixed points ($beta^2 <8pi$) to the infrared limit is in good quantitative agreement with the expected $Delta c=1$ result. The behavior of the $c$-function in the other parts of the flow diagram is also discussed. Finally, we point out that also including higher harmonics in the renormalization group treatment at the level of local potential approximation is not sufficient to give reasonable results, even if the periodicity is taken into account. Rather, incorporating the wave-function renormalization (i. e. going beyond local potential approximation) is crucial to get sensible results even when a single frequency is used.
The Sine-Gordon - equivalently, the massive Thirring - Hamiltonian is ubiquitous in low-dimensional physics, with applications that range from cold atom and strongly correlated systems to quantum impurities. We study here its non-equilibrium dynamics using the quantum quench protocol - following the system as it evolves under the Sine-Gordon Hamiltonian from initial Mott type states with large potential barriers. By means of the Bethe Ansatz we calculate exactly the Loschmidt amplitude, the fidelity and work distribution characterizing these quenches for different values of the interaction strength. Some universal features are noted as well as an interesting duality relating quenches in different parameter regimes of the model.
We study in general the time-evolution of correlation functions in a extended quantum system after the quench of a parameter in the hamiltonian. We show that correlation functions in d dimensions can be extracted using methods of boundary critical phenomena in d+1 dimensions. For d=1 this allows to use the powerful tools of conformal field theory in the case of critical evolution. Several results are obtained in generic dimension in the gaussian (mean-field) approximation. These predictions are checked against the real-time evolution of some solvable models that allows also to understand which features are valid beyond the critical evolution. All our findings may be explained in terms of a picture generally valid, whereby quasiparticles, entangled over regions of the order of the correlation length in the initial state, then propagate with a finite speed through the system. Furthermore we show that the long-time results can be interpreted in terms of a generalized Gibbs ensemble. We discuss some open questions and possible future developments.
We present a modified version of the one-dimensional sine-Gordon that exhibits a thermodynamic, roughening phase transition, in analogy with the 2D usual sine-Gordon model. The model is suited to study the crystalline growth over an impenetrable substrate and to describe the wetting transition of a liquid that forms layers. We use the transfer integral technique to write down the pseudo-Schrodinger equation for the model, which allows to obtain some analytical insight, and to compute numerically the free energy from the exact transfer operator. We compare the results with Monte Carlo simulations of the model, finding a perfect agreement between both procedures. We thus establish that the model shows a phase transition between a low temperature flat phase and a high temperature rough one. The fact that the model is one dimensional and that it has a true phase transition makes it an ideal framework for further studies of roughening phase transitions.
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