We discuss some properties of an integrable and conformally invariant Heisenberg chain with alternating spins S and S' (S'>S) in the presence of a magnetic field. The zero-field magnetic susceptibility is computed and turns out to be only dependent on the spin S. For small enough magnetic field, the low-lying excitations are related to the deformed SU(2) parafermionic field theory at levels 2S and 2(S'-S). Generalizations to these results for other mixed systems are commented on.We discuss some properties of an integrable and conformally invariant Heisenberg chain with alternating spins S and S' (S'>S) in the presence of a magnetic field. The zero-field magnetic susceptibility is computed and turns out to be only dependent on the spin S. For small enough magnetic field, the low-lying excitations are related to the deformed SU(2) parafermionic field theory at levels 2S and 2(S'-S). Generalizations to these results for other mixed systems are commented on.

Journal of Physics A Mathematical and GeneralDec 21, 199320 citations

CONFORMAL QUANTUM FIELD THEORIES AND INTEGRABLE SYSTEMS

M. Karowski

Elsevier eBooksJan 1, 19893 citations

Conformal invariance and integrable theories

Hector J. de Vega, M. Karowski

Nuclear Physics BJan 1, 198773 citations

Parafermionization, bosonization, and critical parafermionic theories

Yuan Yao, Akira Furusaki

Abstract We formulate a ℤk-parafermionization/bosonization scheme for one-dimensional lattice models and field theories on a torus, starting from a generalized Jordan-Wigner transformation on a lattice, which extends the Majorana-Ising duality atk= 2. The ℤk-parafermionization enables us to investigate the critical theories of parafermionic chains whose fundamental degrees of freedom are parafermionic, and we find that their criticality cannot be described by any existing conformal field theory. The modular transformations of these parafermionic low-energy critical theories as general consistency conditions are found to be unconventional in that their partition functions on a torus transform differently from any conformal field theory whenk >2. Explicit forms of partition functions are obtained by the developed parafermionization for a large class of critical ℤk-parafermionic chains, whose operator contents are intrinsically distinct from any bosonic or fermionic model in terms of conformal spins and statistics. We also use the parafermionization to exhaust all the ℤk-parafermionic minimal models, complementing earlier works on fermionic cases.Abstract We formulate a ℤk-parafermionization/bosonization scheme for one-dimensional lattice models and field theories on a torus, starting from a generalized Jordan-Wigner transformation on a lattice, which extends the Majorana-Ising duality atk= 2. The ℤk-parafermionization enables us to investigate the critical theories of parafermionic chains whose fundamental degrees of freedom are parafermionic, and we find that their criticality cannot be described by any existing conformal field theory. The modular transformations of these parafermionic low-energy critical theories as general consistency conditions are found to be unconventional in that their partition functions on a torus transform differently from any conformal field theory whenk >2. Explicit forms of partition functions are obtained by the developed parafermionization for a large class of critical ℤk-parafermionic chains, whose operator contents are intrinsically distinct from any bosonic or fermionic model in terms of conformal spins and statistics. We also use the parafermionization to exhaust all the ℤk-parafermionic minimal models, complementing earlier works on fermionic cases.

arXiv:2012.07529Journal of High Energy PhysicsApr 1, 202125 citations

The intrinsic coupling in integrable quantum field theories

J. Balog, Max R. Niedermaier, F. Niedermayer +3 more

arXiv:hep-th/0001097Nuclear Physics BSep 1, 200019 citations

Energy transport in an integrable parafermionic chain via generalized hydrodynamics

Leonardo Mazza, Jacopo Viti, Matteo Carrega +2 more

We study energy transport in the integrable ${\mathbb{Z}}_{3}$ parafermionic chain using the partitioning protocol. By exploiting the Bethe-ansatz solution for the thermodynamics of the system, we develop a generalized hydrodynamic description of the nonequilibrium steady states, which we benchmark using numerical simulations based on matrix product states. The model features a low-energy conformal limit with central charge $c=\frac{4}{5}$ , which affects the low-temperature energy current, as we explicitly show. Moreover, we exploit that, for energies close to the maximally excited state, the system is also critical and described by a conformal field theory with $c=1$ . By considering the two halves prepared at two temperatures both low in value but opposite in sign, we are able to investigate in an exact and controlled way the junction between two conformal field theories with different central charges. Notwithstanding the absence of global conformal invariance, we find results that approximate to a high degree those of out-of-equilibrium conformal field theories. Our study extends the generalized hydrodynamics to a framework where it can be profitably used for exploring new physical phenomena.We study energy transport in the integrable ${\mathbb{Z}}_{3}$ parafermionic chain using the partitioning protocol. By exploiting the Bethe-ansatz solution for the thermodynamics of the system, we develop a generalized hydrodynamic description of the nonequilibrium steady states, which we benchmark using numerical simulations based on matrix product states. The model features a low-energy conformal limit with central charge $c=\frac{4}{5}$, which affects the low-temperature energy current, as we explicitly show. Moreover, we exploit that, for energies close to the maximally excited state, the system is also critical and described by a conformal field theory with $c=1$. By considering the two halves prepared at two temperatures both low in value but opposite in sign, we are able to investigate in an exact and controlled way the junction between two conformal field theories with different central charges. Notwithstanding the absence of global conformal invariance, we find results that approximate to a high degree those of out-of-equilibrium conformal field theories. Our study extends the generalized hydrodynamics to a framework where it can be profitably used for exploring new physical phenomena.

arXiv:1804.04476Physical review. B./Physical review. BAug 22, 201863 citations

We study energy transport in the integrable

{\mathbb{Z}}_{3}

parafermionic chain using the partitioning protocol. By exploiting the Bethe-ansatz solution for the thermodynamics of the system, we develop a generalized hydrodynamic description of the nonequilibrium steady states, which we benchmark using numerical simulations based on matrix product states. The model features a low-energy conformal limit with central charge

c=\frac{4}{5}

, which affects the low-temperature energy current, as we explicitly show. Moreover, we exploit that, for energies close to the maximally excited state, the system is also critical and described by a conformal field theory with

c=1

. By considering the two halves prepared at two temperatures both low in value but opposite in sign, we are able to investigate in an exact and controlled way the junction between two conformal field theories with different central charges. Notwithstanding the absence of global conformal invariance, we find results that approximate to a high degree those of out-of-equilibrium conformal field theories. Our study extends the generalized hydrodynamics to a framework where it can be profitably used for exploring new physical phenomena.