scholarly journals Exact thermal properties of free-fermionic spin chains

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Michał Białończyk ◽  
Fernando Gómez-Ruiz ◽  
Adolfo del Campo
Keyword(s):  
Algebraic Approach ◽  
Transverse Field ◽  
Spin Chains ◽  
One Dimensional ◽  
Thermal Distribution ◽  
Full Counting Statistics ◽  
Integrable Spin ◽  
Counting Statistics ◽  
Integrable Spin Chains ◽  
The One

An exact description of integrable spin chains at finite temperature is provided using an elementary algebraic approach in the complete Hilbert space of the system. We focus on spin chain models that admit a description in terms of free fermions, including paradigmatic examples such as the one-dimensional transverse-field quantum Ising and XY models. The exact partition function is derived and compared with the ubiquitous approximation in which only the positive parity sector of the energy spectrum is considered. Errors stemming from this approximation are identified in the neighborhood of the critical point at low temperatures. We further provide the full counting statistics of a wide class of observables at thermal equilibrium and characterize in detail the thermal distribution of the kink number and transverse magnetization in the transverse-field quantum Ising chain.

scholarly journals Current operators in integrable spin chains: lessons from long range deformations

2020 ◽  
Vol 8 (2) ◽  
Author(s):  
Balázs Pozsgay
Keyword(s):  
Long Range ◽  
Exact Result ◽  
Spin Chains ◽  
Mean Values ◽  
Heisenberg Spin ◽  
Nested Bethe Ansatz ◽  
Integrable Spin ◽  
Integrable Spin Chains ◽  
The One ◽  
Heisenberg Spin Chains

We consider the finite volume mean values of current operators in integrable spin chains with local interactions, and provide an alternative derivation of the exact result found recently by the author and two collaborators. We use a certain type of long range deformation of the local spin chains, which was discovered and explored earlier in the context of the AdS/CFT correspondence. This method is immediately applicable also to higher rank models: as a concrete example we derive the current mean values in the SU(3)SU(3)-symmetric fundamental model, solvable by the nested Bethe Ansatz. The exact results take the same form as in the Heisenberg spin chains: they involve the one-particle eigenvalues of the conserved charges and the inverse of the Gaudin matrix.

scholarly journals Low-temperature thermodynamics of A2(2) and su(3)-invariant integrable spin chains

1993 ◽  
Vol 406 (3) ◽  
pp. 681-707 ◽  
Author(s):  
Luca Mezincescu ◽  
Rafael I. Nepomechie ◽  
P.K. Townsend ◽  
A.M. Tsvelik
Keyword(s):  
Low Temperature ◽  
Spin Chains ◽  
Integrable Spin ◽  
Integrable Spin Chains

scholarly journals Full Counting Statistics of Laser Excited Rydberg Aggregates in a One-Dimensional Geometry

2014 ◽  
Vol 112 (1) ◽  
Author(s):  
H. Schempp ◽  
G. Günter ◽  
M. Robert-de-Saint-Vincent ◽  
C. S. Hofmann ◽  
D. Breyel ◽  
...  
Keyword(s):  
One Dimensional ◽  
Full Counting Statistics ◽  
Counting Statistics

scholarly journals SUSY field theories in higher dimensions and integrable spin chains

1998 ◽  
Vol 518 (3) ◽  
pp. 689-713 ◽  
Author(s):  
A. Gorsky ◽  
G. Sukov ◽  
A. Mironov
Keyword(s):  
Higher Dimensions ◽  
Spin Chains ◽  
Field Theories ◽  
Integrable Spin ◽  
Integrable Spin Chains

scholarly journals Algebraic approach for the one-dimensional Dirac–Dunkl oscillator

2020 ◽  
Vol 35 (31) ◽  
pp. 2050255
Author(s):  
D. Ojeda-Guillén ◽  
R. D. Mota ◽  
M. Salazar-Ramírez ◽  
V. D. Granados
Keyword(s):  
Energy Spectrum ◽  
Irreducible Representation ◽  
Differential Equations ◽  
Representation Theory ◽  
Algebraic Approach ◽  
The Other ◽  
One Dimensional ◽  
The One

We extend the (1 + 1)-dimensional Dirac–Moshinsky oscillator by changing the standard derivative by the Dunkl derivative. We demonstrate in a general way that for the Dirac–Dunkl oscillator be parity invariant, one of the spinor component must be even, and the other spinor component must be odd, and vice versa. We decouple the differential equations for each of the spinor component and introduce an appropriate su(1, 1) algebraic realization for the cases when one of these functions is even and the other function is odd. The eigenfunctions and the energy spectrum are obtained by using the su(1, 1) irreducible representation theory. Finally, by setting the Dunkl parameter to vanish, we show that our results reduce to those of the standard Dirac-Moshinsky oscillator.

scholarly journals Markovian and Non-Markovian Dynamics in the One-Dimensional Transverse-Field XY Model

2019 ◽  
Vol 176 (2) ◽  
pp. 492-504
Author(s):  
Z. Saghafi ◽  
S. Mahdavifar ◽  
E. Hosseini Lapasar
Keyword(s):  
Transverse Field ◽  
Xy Model ◽  
One Dimensional ◽  
Markovian Dynamics ◽  
The One
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