# Asymptotic behavior of Toeplitz determinants with delta function singularities

@article{Maric2020AsymptoticBO, title={Asymptotic behavior of Toeplitz determinants with delta function singularities}, author={Vanja Mari'c and F. Franchini}, journal={arXiv: Mathematical Physics}, year={2020} }

We find the asymptotic behaviors of Toeplitz determinants with symbols which are a sum of two contributions: one analytical and non-zero function in an annulus around the unit circle, and the other proportional to a Dirac delta function. The formulas are found by using the Wiener-Hopf procedure. The determinants of this type are found in computing the spin-correlation functions in low-lying excited states of some integrable models, where the delta function represents a peak at the momentum of… Expand

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#### References

SHOWING 1-10 OF 26 REFERENCES

Aspects of Toeplitz Determinants

- Mathematics, Physics
- 2011

We review the asymptotic behavior of a class of Toeplitz (as well as related Hankel and Toeplitz + Hankel) determinants which arise in integrable models and other contexts. We discuss Szego,… Expand

Theory of Toeplitz Determinants and the Spin Correlations of the Two-Dimensional Ising Model. III

- Physics
- 1967

We consider the rectangular Ising model on a half-plane of infinite extent and study some of the consequences connected with the presence of the boundary. Only the spins on the boundary row are… Expand

Quantum Ising chains with boundary fields

- Physics, Mathematics
- 2015

We present a detailed study of the finite one-dimensional quantum Ising chain in a transverse field in the presence of boundary magnetic fields coupled with the order-parameter spin operator. We… Expand

An Introduction to Integrable Techniques for One-Dimensional Quantum Systems

- Physics, Mathematics
- 2017

This monograph introduces the reader to basic notions of integrable techniques for one-dimensional quantum systems. In a pedagogical way, a few examples of exactly solvable models are worked out to… Expand

The Frustration of being Odd: Universal Area Law violation in local systems.

- Mathematics
- 2019

At the core of every frustrated system, one can identify the existence of frustrated rings that are usually interpreted in terms of single--particle physics. We check this point of view through a… Expand

Rigorous proof for the nonlocal correlation function in the transverse Ising model with ring frustration.

- Mathematics, Medicine
- Physical review. E
- 2018

It is proved that all the low excited energy states forming the gapless kink phase share the same asymptotic correlation function with the ground state, and the thermal correlation function almost remains constant at low temperatures if one assumes a canonical ensemble. Expand

Quantum transitions driven by one-bond defects in quantum Ising rings.

- Physics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2015

It is shown that the quantum scaling phenomena driven by lower-dimensional defects in quantum Ising-like models shows a universal scaling behavior, which is characterized by computing, either analytically or numerically, scaling functions for the low-level energy differences and the two-point correlation function. Expand

The two dimensional Ising model

- 2016

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… Expand

Two Soluble Models of an Antiferromagnetic Chain

- Physics
- 1961

Two genuinely quantum mechanical models for an antiferromagnetic linear chain with nearest neighbor interactions are constructed and solved exactly, in the sense that the ground state, all the… Expand

Asymptotic behavior of Toeplitz matrices and determinants

- Mathematics
- 1969

AbstractWe consider the inverse XN and determinant DN(c) of an N×N Toeplitz matrix CN=[ci−j]0N−1as N ar∞. Under the condition that there exists a monotonic decreasing summable bound bn≧|cn|+|c−n|,… Expand