Quantum inverse problem method. I

Experimental characterization of a quantum many-body system via higher-order correlations

“…This characterises the essential features of the system, the relevant quasiparticles, their interactions and possible topologically distinct vacua. We verify that in thermal equilibrium the physics can be described by the quantum sine-Gordon model [3][4][5][6], relevant for a wide variety of disciplines from particle to condensed-matter physics [7][8][9]. Our experiment establishes a general method to analyse quantum many-body systems in experiments.…”

Quantum and classical integrable sine-Gordon model with defect

“…Recall that [11] for quantum integrability the monodromy matrix of the system (5.63) must satisfy the global version of the quantum YBE (QYBE) (…”

“…Following the formulation of quantum SG model [11] we can apply the algebraic Bethe ansatz method to the lattice regularized quantum DSG constructed above and solve in principle its eigenvalue problem exactly. Recall that the aim of the algebraic Bethe ansatz is to solve exactly the eigenvalue problem of τ (ξ) = trace T (ξ), T (ξ) = j L j (ξ ), generating all conserved operators including the Hamiltonian, in the form: τ (ξ)|n = Λ(ξ )|n , with the eigenstates |n defined as |n = |ξ 1 , .…”

“…T 12 (ξ ) = B(ξ ) acts as creation operator, while T 21 (ξ ) = C(ξ ) as destruction operator annihilating the pseudovacuum: C(ξ )|0 = 0. A crucial step in this formalism is to construct the pseudovacuum state |0 , which is achieved for the SG model by combining the actions of consecutive pair of Lax operators: U j U j +1 |0 [11]. Repeating this procedure we can construct the pseudovacuum |0 ± = ± N 2 j =±1 |Ω (2) j for the quantum DSG model, yielding C ± (λ)|0 ± = 0, for all sites except the defect point at j = 0.…”

Off-diagonal Bethe ansatz solution of the XXX spin chain with arbitrary boundary conditions

“…Since Yang and Baxter's pioneering works [4,5,1], the quantum Yang-Baxter equation (QYBE), which define the underlying algebraic structure, has become a cornerstone for constructing and solving the integrable models. There are several well-known methods for deriving the Bethe ansatz (BA) solution of integrable models: the coordinate BA [6,1,7,8,9], the T-Q approach [1,10], the algebraic BA [11,12,13], the analytic BA [14], the functional BA [15] and others [16,17,18,19,20,21,22,23,24,25,26,27,28,29].…”