The a-cycle problem for transverse Ising ring

@article{Dong2016TheAP,
  title={The a-cycle problem for transverse Ising ring},
  author={Jian-Jun Dong and Peng Li and Qi-Hui Chen},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
  year={2016},
  volume={2016}
}
Traditionally, the transverse Ising model is mapped to the fermionic c-cycle problem, which neglects the boundary effect due to thermodynamic limit. If persisting on a perfect periodic boundary condition, we can get a so-called a-cycle problem that has not been treated seriously so far (Lieb et al 1961 Ann. Phys. 16 407). In this work, we show a little surprising but exact result in this respect. We find the odevity of the number of lattice sites, N, in the a-cycle problem plays an unexpected… 

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References

SHOWING 1-10 OF 31 REFERENCES

Two-Dimensional Ising Model as a Soluble Problem of Many Fermions

The two-dimensional Ising model for a system of interacting spins (or for the ordering of an AB alloy) on a square lattice is one of the very few nontrivial many-body problems that is exactly soluble

The two-dimensional Ising model

In this thesis the equivalence of the two-dimensional critical classical Ising model in the scaling limit without a magnetic field, the (one-dimensional) critical quantum Ising chain in the scaling

Entanglement entropy and quantum field theory

We carry out a systematic study of entanglement entropy in relativistic quantum field theory. This is defined as the von Neumann entropy SA = −Tr ρAlogρA corresponding to the reduced density matrix

Finite-size scaling of the entanglement entropy of the quantum Ising chain with homogeneous, periodically modulated and random couplings

Using free-fermionic techniques we study the entanglement entropy of a block of contiguous spins in a large finite quantum Ising chain in a transverse field, with couplings of different types:

Universality of entropy scaling in one dimensional gapless models.

An explicit formula for the entropy of the subsystem at any temperature is obtained by means of conformal field theory and the second law of thermodynamics and is universal.

Quantum phase transitions

Abstract We give a general introduction to quantum phase transitions in strongly correlated electron systems. These transitions, which occur at zero temperature when a non-thermal parameter g such as