Nonlinear integral equations for the $\mathrm{SL}(2,\mathbb {R})/\mathrm{U}(1)$ black hole sigma modelNonlinear integral equations for the $\mathrm{SL}(2,\mathbb {R})/\mathrm{U}(1)$ black hole sigma model

Constantin Candu, Yacine Ikhlef

It was previously established that the critical staggered XXZ spin chain provides a lattice regularization of the black hole conformal field theory (CFT). We reconsider the continuum limit of this spin chain with the exact method of nonlinear integral equations (NLIEs), paying particular attention to the effects of a singular integration kernel. With the help of the NLIEs, we rederive the continuous black hole spectrum, but also numerically match the density of states of the spin chain with that of the CFT, which is a new result. Finally, we briefly discuss the integrable structure of the black hole CFT and the identification of its massive integrable perturbation on the lattice.It was previously established that the critical staggered XXZ spin chain provides a lattice regularization of the black hole conformal field theory (CFT). We reconsider the continuum limit of this spin chain with the exact method of nonlinear integral equations (NLIEs), paying particular attention to the effects of a singular integration kernel. With the help of the NLIEs, we rederive the continuous black hole spectrum, but also numerically match the density of states of the spin chain with that of the CFT, which is a new result. Finally, we briefly discuss the integrable structure of the black hole CFT and the identification of its massive integrable perturbation on the lattice.

arXiv:1306.2646Journal of Physics A Mathematical and TheoreticalSep 27, 201340 citations

Machine-defined lattice spin models

C. H. Woo

Physics Letters AJun 1, 19861 citation

Numerical methods for spin models

Antônio Sérgio Teixeira Pires

Institute of Physics eBooksApr 1, 20213 citations

Path-integral representation for quantum spin models: Application to the quantum cavity method and Monte Carlo simulations

Florent Krząkała, Alberto Rosso, Guilhem Semerjian +1 more

The cavity method is a well-established technique for solving classical spin models on sparse random graphs (mean-field models with finite connectivity). Laumann et al. [Phys. Rev. B 78, 134424 (2008)] proposed recently an extension of this method to quantum spin-1/2 models in a transverse field, using a discretized Suzuki-Trotter imaginary-time formalism. Here we show how to take analytically the continuous imaginary-time limit. Our main technical contribution is an explicit procedure to generate the spin trajectories in a path-integral representation of the imaginary-time dynamics. As a side result we also show how this procedure can be used in simple heat bath Monte Carlo simulations of generic quantum spin models. The replica symmetric continuous-time quantum cavity method is formulated for a wide class of models and applied as a simple example on the Bethe lattice ferromagnet in a transverse field. The results of the methods are confronted with various approximation schemes in this particular case. On this system we performed quantum Monte Carlo simulations that confirm the exactness of the cavity method in the thermodynamic limit.The cavity method is a well-established technique for solving classical spin models on sparse random graphs (mean-field models with finite connectivity). Laumann et al. [Phys. Rev. B 78, 134424 (2008)] proposed recently an extension of this method to quantum spin-1/2 models in a transverse field, using a discretized Suzuki-Trotter imaginary-time formalism. Here we show how to take analytically the continuous imaginary-time limit. Our main technical contribution is an explicit procedure to generate the spin trajectories in a path-integral representation of the imaginary-time dynamics. As a side result we also show how this procedure can be used in simple heat bath Monte Carlo simulations of generic quantum spin models. The replica symmetric continuous-time quantum cavity method is formulated for a wide class of models and applied as a simple example on the Bethe lattice ferromagnet in a transverse field. The results of the methods are confronted with various approximation schemes in this particular case. On this system we performed quantum Monte Carlo simulations that confirm the exactness of the cavity method in the thermodynamic limit.

arXiv:0807.2553Physical Review BOct 30, 200873 citations

Path integral of spin models

Horacio Grinberg

Physics Letters AApr 30, 200310 citations

Functional integral quantisation of an anisotropic spin-field model

Katsuhiro Nakamura, Tomohei Sasada, A. R. Bishop

The authors develop a path-integral formalism to obtain the semiclassical quantum spectrum of the pulse soliton with an internal degree of freedom in the one-dimensional continuous Heisenberg ferromagnet with an easy axis. No restriction is imposed on the spin magnitude S. For S=1/2, the pulse soliton yields the same quantum spectrum as that of the S=1/2 lattice Heisenberg-Ising ferromagnet obtained by the Bethe ansatz method. This agreement supports a plausible particle picture of the multimagnon bound state. For S>1/2, the present semiclassical spectrum can also be interpreted, aside from its prefactor, in terms of an underlying spin S(>1/2) quantum lattice model if the cut-off condition for the wave-number of the soliton is taken into account.The authors develop a path-integral formalism to obtain the semiclassical quantum spectrum of the pulse soliton with an internal degree of freedom in the one-dimensional continuous Heisenberg ferromagnet with an easy axis. No restriction is imposed on the spin magnitude S. For S=1/2, the pulse soliton yields the same quantum spectrum as that of the S=1/2 lattice Heisenberg-Ising ferromagnet obtained by the Bethe ansatz method. This agreement supports a plausible particle picture of the multimagnon bound state. For S>1/2, the present semiclassical spectrum can also be interpreted, aside from its prefactor, in terms of an underlying spin S(>1/2) quantum lattice model if the cut-off condition for the wave-number of the soliton is taken into account.

Journal of Physics C Solid State PhysicsJul 10, 198310 citations

Nonlinear integral equations for the

\mathrm{SL}(2,\mathbb {R})/\mathrm{U}(1)

black hole sigma model