30 citations · 230 across the 51 of their papers we have counts for
52 papers
When Is Kramers-Wannier Duality Invertible?
Akash Sinha, Pramod Padmanabhan, Vladimir Korepin
{\it Kramers-Wannier} duality of the quantum Ising chain is naturally realized as a noninvertible transformation on a finite periodic chain. Upon incorporating appropriate symmetry…
Multiparameter Quantum Affine Spaces and the Scalene Yang--Baxter Equation
Pramod Padmanabhan, Somnath Maity, Vladimir Korepin
We construct representation-independent families of solutions of the non-braided scalene Yang--Baxter equation from quadratic noncommutative algebras. Beginning with two anticommut…
Scalene Yang--Baxter triples as a source of hidden symmetries beyond the ordinary Yang--Baxter equation
Pramod Padmanabhan, Somnath Maity, Vladimir Korepin
We study a nearest-neighbor non-Hermitian spin chain obtained from one member of an exact non-braided scalene Yang--Baxter triple. Its local Hamiltonian density violates both the d…
Symmetries of the Generalized Yang--Baxter Equations
Pramod Padmanabhan, Somnath Maity, Akash Sinha +1
The generalized Yang-Baxter equations are multi-site versions of the standard Yang-Baxter equation. When spectral parameters are included, such equations are expected to lead to in…
Hidden Ising models from the generalized Yang-Baxter equation
Akash Sinha, Somnath Maity, Pramod Padmanabhan +1
We introduce a one dimensional spin Hamiltonian with multi-site interactions, but still local. The algebra of its Hamiltonian densities resembles that of the transver…
Noninvertible Kramers-Wannier duality symmetries for the discrete-time quantum Ising chain
Akash Sinha, Pramod Padmanabhan, Vladimir Korepin
Integrable trotterization} provides a method to evolve a continuous time integrable many-body system in discrete time, such that it retains its conserved quantities. Here we explic…
Clifford Solver for the Tetrahedron Equation and its Variants
Pramod Padmanabhan, Vivek Kumar Singh, Vladimir Korepin
The different forms of the tetrahedron equation appear when all possible ways to label the scattering process of infinitely long straight lines are considered in three dimensional…
Almost local integrable models from supersymmetry algebras
Somnath Maity, Pramod Padmanabhan, Jarmo Hietarinta +1
Supersymmetry algebras can be used to obtain algebraic expressions for constant Yang-Baxter solutions, also known as braid group generators. This was done for non-invertible braid…
The Yang-Baxter integrability of the critical Ising chain
Akash Sinha, Tinu Justin, Pramod Padmanabhan +1
We show that the one dimensional, critical transverse field Ising model is Yang-Baxter integrable. This is done by constructing commuting transfer matrices built out of a -matri…
Non-hermitian integrable systems from constant non-invertible solutions of the Yang-Baxter equation
Somnath Maity, Pramod Padmanabhan, Vladimir Korepin
We construct invertible spectral parameter dependent Yang-Baxter solutions (-matrices) by Baxterizing constant non-invertible Yang-Baxter solutions. The solutions are algebraic…
Non-invertible symmetry breaking in a frustration-free spin chain
Akash Sinha, Vivek Kumar Singh, Pramod Padmanabhan +2
A nearest-neighbor, frustration-free spin chain can be constructed {\it via} projectors of various ranks á la Bravyi-Gosset. We show that in the rank 1 case this syst…
Majorana fermions solve the tetrahedron equations as well as higher simplex equations
Pramod Padmanabhan, Vladimir Korepin
Yang-Baxter equations define quantum integrable models. The tetrahedron and higher simplex equations are multi-dimensional generalizations. Finding the solutions of these equations…
Algebraic classification of Hietarinta's solutions of Yang-Baxter equations~:~invertible operators
Somnath Maity, Vivek Kumar Singh, Pramod Padmanabhan +1
In order to examine the simulation of integrable quantum systems using quantum computers, it is crucial to first classify Yang-Baxter operators. Hietarinta was among the first to c…
Toffoli gates solve the tetrahedron equations
Akash Sinha, Pramod Padmanabhan, Vladimir Korepin
The circuit model of quantum computation can be interpreted as a scattering process. In particular, factorised scattering operators result in integrable quantum circuits that provi…
Solving the Yang-Baxter, tetrahedron and higher simplex equations using Clifford algebras
Pramod Padmanabhan, Vladimir Korepin
Bethe Ansatz was discoverd in 1932. Half a century later its algebraic structure was unearthed: Yang-Baxter equation was discovered, as well as its multidimensional generalizations…
Yang-Baxter solutions from commuting operators
Pramod Padmanabhan, Kun Hao, Vladimir Korepin
We construct -matrices (with a multidimensional spectral parameter) that include additive as well as non-additive parameters. They satisfy the colored Yang-Baxter equation. The…
A stabilizer code model with non-invertible symmetries: Strange fractons, confinement, and non-commutative and non-Abelian fusion rules
Tanay Kibe, Ayan Mukhopadhyay, Pramod Padmanabhan
We introduce a stabilizer code model with a qutrit at every edge on a square lattice and with non-invertible plaquette operators. The degeneracy of the ground state is topological…
Disorder-free localisation in continuous-time quantum walks : Role of symmetries
A. P. Balachandran, Anjali Kundalpady, Pramod Padmanabhan +1
We investigate the phenomenon of disorder-free localisation in quantum systems with global permutation symmetry. We use permutation group theory to systematically construct permuta…
Dyck Paths and Topological Quantum Computation
Vivek Kumar Singh, Akash Sinha, Pramod Padmanabhan +1
The fusion basis of Fibonacci anyons supports unitary braid representations that can be utilized for universal quantum computation. We show a mapping between the fusion basis of th…
Groupoid Toric Codes
Pramod Padmanabhan, Indrajit Jana
The toric code can be constructed as a gauge theory of finite groups on oriented two dimensional lattices. Here we construct analogous models with the gauge fields belonging to gro…
Loop braid groups and integrable models
Pramod Padmanabhan, Abhishek Chowdhury
Loop braid groups characterize the exchange of extended objects, namely loops, in three dimensional space generalizing the notion of braid groups that describe the exchange of poin…
Topological Quantum Computation on Supersymmetric Spin Chains
Indrajit Jana, Filippo Montorsi, Pramod Padmanabhan +1
Quantum gates built out of braid group elements form the building blocks of topological quantum computation. They have been extensively studied in quantum group theories,…
Non-CSS color codes on 2D lattices : Models and Topological Properties
Pramod Padmanabhan, Abhishek Chowdhury, Fumihiko Sugino +2
The two-dimensional color code is an alternative to the toric code that encodes more logical qubits while maintaining crucial features of the toric…
Novel quantum phases on graphs using abelian gauge theory
Pramod Padmanabhan, Fumihiko Sugino
Graphs are topological spaces that include broader objects than discretized manifolds, making them interesting playgrounds for the study of quantum phases not realized by symmetry…