30 citations · 230 across the 51 of their papers we have counts for
22 papers · 1 filter
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…
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…
Many-body localization in large-N conformal mechanics
Fumihiko Sugino, Pramod Padmanabhan
In quantum statistical mechanics, closed many-body systems that do not exhibit thermalization after an arbitrarily long time in spite of the presence of interactions are called as…
Supersymmetric Many-Body Systems from Partial Symmetries: Integrability, Localization and Scrambling
Pramod Padmanabhan, Soo-Jong Rey, Daniel Teixeira +1
Partial symmetries are described by generalized group structures known as symmetric inverse semigroups. We use the algebras arising from these structures to realize supersymmetry i…
Toric code-like models from the parameter space of lattice gauge theories
Miguel Jorge Bernabe Ferreira, Pramod Padmanabhan, Paulo Teotonio-Sobrinho
A state sum construction on closed manifolds á la Kuperberg can be used to construct the partition functions of lattice gauge theories based on involutory Hopf algebras, $\mat…
Lehmann-Symanzik-Zimmermann S-Matrix elements on the Moyal Plane
A. P. Balachandran, Pramod Padmanabhan, Amilcar R. de Queiroz
Field theories on the Groenewold-Moyal(GM) plane are studied using the Lehmann-Symanzik-Zimmermann(LSZ) formalism. The example of real scalar fields is treated in detail. The S-mat…
Unusual Thermodynamics on the Fuzzy 2-Sphere
Sanatan Digal, Pramod Padmanabhan
Higher spin Dirac operators on both the continuum sphere() and its fuzzy analog() come paired with anticommuting chirality operators. A consequence of this is seen in t…
Non-Pauli Effects from Noncommutative Spacetimes
A. P. Balachandran, Pramod Padmanabhan
Noncommutative spacetimes lead to nonlocal quantum field theories (qft's) where spin-statistics theorems cannot be proved. For this reason, and also backed by detailed arguments, i…
Spectrum of Spin 1 Dirac Operators on the Fuzzy 2-Sphere
Sanatan Digal, Pramod Padmanabhan
We numerically find out the spectrum of the spin Dirac operators found in~\cite{ApbPP}. We give an analytic and numerical proof that they are unitarily inequivalent. Since…
Non-Pauli Transitions From Spacetime Noncommutativity
A. P. Balachandran, Anosh Joseph, Pramod Padmanabhan
There are good reasons to suspect that spacetime at Planck scales is noncommutative. Typically this noncommutativity is controlled by fixed "vectors" or "tensors" with numerical en…
The Groenewold - Moyal Plane and its Quantum Physics
A. P. Balachandran, Pramod Padmanabhan
Quantum theories constructed on the noncommutative spacetime called the Groenewold-Moyal(GM) plane exhibit many interesting properties such as causality violation, Lorentz and CPT…
Spin Dirac Operators on the Fuzzy 2-Sphere
A. P. Balachandran, Pramod Padmanabhan
The spin 1/2 Dirac operator and its chirality operator on the fuzzy 2-sphere can be constructed using the Ginsparg-Wilson(GW) algebra [arxiv:hep-th/0511114]. This construct…
Beyond fuzzy spheres
T. R. Govindarajan, Pramod Padmanabhan, T. Shreecharan
We study polynomial deformations of the fuzzy sphere, specifically given by the cubic or the Higgs algebra. We derive the Higgs algebra by quantizing the Poisson structure on a sur…
Causality and statistics on the Groenewold-Moyal plane
A. P. Balachandran, Anosh Joseph, Pramod Padmanabhan
Quantum theories constructed on the noncommutative spacetime called the Groenewold-Moyal plane exhibit many interesting properties such as Lorentz and CPT noninvariance, causality…