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We associate geometric partial differential equations on holomorphic vector bundles to Bridgeland stability conditions. We call solutions to these equations $Z$-critical connections, with $Z$ a central charge. Deformed Hermitian Yang--Mills…

Differential Geometry · Mathematics 2024-01-23 Ruadhaí Dervan , John Benjamin McCarthy , Lars Martin Sektnan

The Quantum Inverse Scattering Method is a scheme for solving integrable models in $1+1$ dimensions, building on an $R$-matrix that satisfies the Yang--Baxter equation and in terms of which one constructs a commuting family of transfer…

Mathematical Physics · Physics 2023-07-13 Xavier Poncini , Jorgen Rasmussen

In general relativity, the motion of an extended body moving in a given spacetime can be described by a particle on a (generally non-geodesic) worldline. In first approximation, this worldline is a geodesic of the underlying spacetime, and…

General Relativity and Quantum Cosmology · Physics 2024-02-05 Paul Ramond

The dense O(1) loop model is a statistical physics model with connections to the quantum XXZ spin chain, alternating sign matrices, the six-vertex model and critical bond percolation on the square lattice. When cylindrical boundary…

Mathematical Physics · Physics 2017-03-14 Ron Peled , Dan Romik

In integrable one-dimensional quantum systems an infinite set of local conserved quantities exists which can prevent a current from decaying completely. For cases like the spin current in the XXZ model at zero magnetic field or the charge…

Strongly Correlated Electrons · Physics 2011-01-31 J. Sirker , R. G. Pereira , I. Affleck

A detailed study of an $S={1\over2}$ spin ladder model is given. The ladder consists of plaquettes formed by nearest neighbor rungs with all possible SU(2)-invariant interactions. For properly chosen coupling constants, the model is shown…

Condensed Matter · Physics 2009-10-31 S. Albeverio , S. M. Fei , Y. P. Wang

We consider a unitary circuit where the underlying gates are chosen to be R-matrices satisfying the Yang-Baxter equation and correlation functions can be expressed through a transfer matrix formalism. These transfer matrices are no longer…

Quantum Physics · Physics 2022-01-12 Pieter W. Claeys , Jonah Herzog-Arbeitman , Austen Lamacraft

The $N$ site open XXZ quantum spin chain with a right non-diagonal boundary and special diagonal left boundary is considered. The boundary non-local charges originally obtained from a field theoretical viewpoint, for the sine Gordon model…

Mathematical Physics · Physics 2009-11-10 Anastasia Doikou

The ground state of Shor-Movassagh chain can be analytically described by the Motzkin paths. There is no analytical description of the excited states, the model is not solvable. We prove the integrability of the model without interacting…

Mathematical Physics · Physics 2021-09-22 Bin Tong , Olof Salberger , Kun Hao , Vladimir Korepin

We calculate the scalar product of Bethe states of the XXZ spin-$\frac{1}{2}$ chain with general integrable boundary conditions. The off-shell equations satisfied by the transfer matrix and the off-shell Bethe vectors allow one to derive a…

Mathematical Physics · Physics 2021-09-01 Samuel Belliard , Rodrigo A. Pimenta , Nikita A. Slavnov

We have found a family of solvable nineteen vertex model with statistical configurations invariant by the time reversal symmetry within a systematic study of the respective Yang-Baxter relation. The Boltzmann weights sit on a degree seven…

Mathematical Physics · Physics 2015-05-20 M. J. Martins

In this paper and its sequel, we construct topologically invariant defects in two-dimensional classical lattice models and quantum spin chains. We show how defect lines commute with the transfer matrix/Hamiltonian when they obey the defect…

Statistical Mechanics · Physics 2017-09-11 David Aasen , Roger S. K. Mong , Paul Fendley

We describe integrable elliptic q-deformed anisotropic long-range spin chain. The derivation is based on our recent construction for commuting anisotropic elliptic spin Ruijsenaars-Macdonald operators. We prove that the Polychronakos…

Mathematical Physics · Physics 2022-12-09 M. Matushko , A. Zotov

We derive an explicit mapping between the spectra of conserved local operators of integrable quantum lattice models and the density distributions of their thermodynamic particle content. This is presented explicitly for the Heisenberg XXZ…

Statistical Mechanics · Physics 2016-06-06 Enej Ilievski , Eoin Quinn , Jacopo De Nardis , Michael Brockmann

The integrability of a quantum many-body system, which is characterized by the presence or absence of local conserved quantities, drastically impacts the dynamics of isolated systems, including thermalization. Nevertheless, a rigorous and…

Statistical Mechanics · Physics 2025-04-15 Akihiro Hokkyo

We find an integrable generalization of the BCS model with non-uniform Coulomb and pairing interaction. The Hamiltonian is integrable by construction since it is a functional of commuting operators; these operators, which therefore are…

Superconductivity · Physics 2007-05-23 Luigi Amico , Antonio Di Lorenzo , Andreas Osterloh

Motivated by a study of the crossing symmetry of the `gemini' representation of the affine Hecke algebra we give a construction for crossing tensor space representations of ordinary Hecke algebras. These representations build solutions to…

High Energy Physics - Theory · Physics 2009-11-11 Anastasia Doikou , Paul P. Martin

We investigate emergent quantum dynamics of the tilted Ising chain in the regime of a weak transverse field. Within the leading order perturbation theory, the Hilbert space is fragmented into exponentially many decoupled sectors. We find…

Strongly Correlated Electrons · Physics 2022-05-17 Alvise Bastianello , Umberto Borla , Sergej Moroz

A general method for solving the so-called quantum inverse scattering problem (namely the reconstruction of local quantum (field) operators in term of the quantum monodromy matrix satisfying a Yang-Baxter quadratic algebra governed by an…

High Energy Physics - Theory · Physics 2009-10-31 J. M. Maillet , V. Terras

We study a Yang-Baxter integrable quantum spin-1/2 chain with random interactions. The Hamiltonian is local and involves two and three-spin interactions with random parameters. We show that the energy eigenstates of the model are never…

Disordered Systems and Neural Networks · Physics 2018-09-27 Fabian H. L. Essler , Rianne van den Berg , Vladimir Gritsev