# 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

- Physics
- 1964

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

- PhysicsFrom Quarks to Pions
- 2018

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

- Physics
- 2004

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

- Physics
- 2008

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.

- PhysicsPhysical review letters
- 2004

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

- Physics
- 2001

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…