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Chapter
The Algebraic Bethe Ansatz
The algebraic Bethe Ansatz method for quantum integrable models was proposed by the Leningrad Group [1–7] in the late 1970s, based on YBE. This method was then generalized to open boundary integrable systems by S...
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Chapter
The Spin- \(\frac{1}{2}\) Torus
The spin- \(\frac{1}{2}\) torus model describes the anisotropic spin chain with antiperiodic boundary conditions or a Möbius-like topological bounda...
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Chapter
The One-Dimensional Hubbard Model
As one of the minimal models for strongly correlated electron systems, the Hubbard model plays a central role in modern condensed matter physics.
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Chapter
The Hierarchical Off-Diagonal Bethe Ansatz
The integrable in higher dimensional quantum space are particularly interesting because of their important applications in quantum field theory.
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Chapter
Overview
Quantum integrable models are exactly solvable models defined by the Yang-Baxter equation (YBE) [1, 2] or the Lax representation [3].
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Chapter
The Periodic Anisotropic Spin- \(\frac{1}{2}\) Chains
Based on the pioneering work of Bethe [1] in which the coordinate Bethe Ansatz method was invented and the exact solution of the spin- \(\frac{1}{2}\) ...
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Chapter
The Spin- \(\frac{1}{2}\) Chains with Arbitrary Boundary Fields
A quantum integrable model with open boundary condition was first solved via the cordinate Bethe Ansatz method by Gaudin [1].
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Chapter
The Nested Off-Diagonal Bethe Ansatz
In Chap. 2, introduced how the nested algebraic Bethe Ansatz method was used in the exact solution of the periodic \(SU(n)\) -invariant spin chain. This method can also solve the open chain with diagonal...
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Chapter
The Izergin-Korepin Model
The integrable models can be classified into several series such as \(A_n\) -, \(B_n\) ...
