arXiv subjects

Rudranil Basu

Publications and source records attributed to Rudranil Basu.

At least 19 recordsLinked to original sources

arXiv2026

Krylov Complexity: Flat bands and Carroll breaking deformations

Systems with flat band structures, when written in the language of Compact Localised States (CLS), have been shown to be explicitly invariant under supertranslation symmetries, making Carrollian symmetries inherently important for such systems. In this work, we explore the state dynamics of these systems, focusing on quenches induced by Carroll breaking perturbations, through the probe of Krylov (spread) Complexity. We specialise to Fermionic ladder Hamiltonians with all bands flat (ABF) scenario, augmented by a supertranslation preserving interaction, and discuss Krylov state complexity for quenches across critical lines. We further discuss how the growth of Krylov complexity sharply resolves the phase-dependent resilience of Carrollian sectors against delocalising perturbations. This is augmented by a complementary mechanism for Krylov growth in a continuum Carroll scalar field theory with a gradient deformation, which exhibits strong ultraviolet sensitivity (UV/IR mixing).

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arXiv2025

Probing Topological Phases in a Strongly Correlated Ladder Model via Entanglement

The interplay between non-trivial band topology and strong electronic correlations is a central challenge in modern condensed matter physics. We investigate this competition on a two-leg ladder model with a p-wave-like hybridisation between the legs. This model hosts a symmetry-protected topological phase in its non-interacting limit. Using the density-matrix renormalisation group algorithm, we compute the comprehensive quantum phase diagram in the presence of a repulsive inter-leg density-density interaction. Our analysis, based on entanglement entropy and the entanglement spectrum, reveals a fascinating dichotomy in the stability of the topological phase. We find a non-trivial change in the value of the edge entanglement entropy as we include interaction. Furthermore, we find that the phase boundary separating a trivial insulator phase and a topological one with winding number two remains robustly pinned at its non-interacting location, irrespective of the interaction strength. Variation of the effective conformal field theory's central charge near the critical line explains the robustness of the gap. In contrast, the transition to an insulating phase with winding number one is heavily renormalised, with the critical line shifting significantly as the interaction increases. By successfully mapping the phase diagram and identifying the distinct behaviours of the phase boundaries, our work clarifies how interactions can selectively preserve or destroy different aspects of a topological phase.

cond-mat.str-el↗

arXiv2025

Light and Shadow OPEs: A Carroll Symmetric Approach to Flat Holography

In this work, we fix the leading term in the operator algebra of light-transformed operators in the context of flat space holography. Starting with light-transformed graviton correlators, we show that the OPE obtained by taking the collinear limit satisfies translation symmetry at the leading order not independently but with assistance from the sub-leading order. Motivated by this result, we start with a general CFT-like ansatz for the OPE and, by keeping track of the sub-leading term, derive an expression for the scaling dimension of the operator appearing in the leading term. We further show that we can fix the OPE coefficient corresponding to this term as well. We use this result to find the OPE for well-studied theories like gravity, Yang-Mills and Einstein-Yang-Mills theory, and find that the scaling dimension found from our formula matches with the one obtained by looking at the collinear limit of bulk momentum space vertices. We initiate a similar study for operators in the shadow basis by looking at the OPE of shadow-transformed graviton correlators.

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arXiv2024

Flat Bands and Compact Localised States: A Carrollian roadmap

We show how Carrollian symmetries become important in the construction of one-dimensional fermionic systems with all flat-band spectra from first principles. The key ingredient of this construction is the identification of Compact Localised States (CLSs), which appear naturally by demanding $\textit{supertranslation}$ invariance of the system. We use CLS basis states, with inherent $\textit{ultra-local}$ correlations, to write down an interacting theory which shows a non-trivial phase structure and an emergent Carroll conformal symmetry at the gapless points. We analyze this theory in detail for both zero and finite chemical potential.

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arXiv2024

Light transformation: A Celestial and Carrollian perspective

In this paper, we first study the consequence of spacetime translations and Lorentz transformations on Celestial CFT OPEs. Working with the light transforms of the operators belonging to the modified Mellin basis, we found that the leading order singularity in the OPE of such operators could be fixed purely using Poincar\'e symmetries owing to the non-trivial action of the translations on these operators. The OPE coefficient is then fixed using the soft limit of the correlation functions. We check that this singular structure obtained from symmetries is consistent with the OPE limit of three-point functions. This approach could potentially be useful for studying Celestial CFT without adverting to bulk physics. As another goal, we explore the significance of light transformation in Carrollian CFTs. In the special cases we considered, we show that light transformation equips us with a map between two branches of Carroll CFT in $d=3$ dimension at the level of correlation functions in the near coincident limit.

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arXiv2024

Symmetry Resolution in non-Lorentzian Field Theories

Starting from the computation of Symmetry Resolved Entanglement Entropy (SREE) for boosted intervals in a two dimensional Conformal Field Theory, we compute the same in various non-Lorentzian limits, viz, Galilean and Carrollian Conformal Field Theory in same number of dimensions. We approach the problem both from a limiting perspective and by using intrinsic symmetries of respective non-Lorentzian conformal algebras. In particular, we calculate the leading order terms, logarithmic terms, and the $\mathcal{O}(1)$ terms and explicitly show exact compliance with $\textit{equipartition of entanglement}$, even in the non-Lorentzian system. Keeping in mind the holographic origin of SREE for the Carrollian limit, we further compute SREE for BMS$_{3}$-Kac-Moody, which couples a $U(1)\times U(1)$ theory with bulk gravity.

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arXiv2023

Entanglement of edge modes in (very) strongly correlated topological insulators

Identifying topological phases for a strongly correlated theory remains a non-trivial task, as defining order parameters, such as Berry phases, is not straightforward. Quantum information theory is capable of identifying topological phases for a theory that exhibits quantum phase transition with a suitable definition of order parameters that are related to different entanglement measures for the system. In this work, we study entanglement entropy for a bi-layer SSH model, both in the presence and absence of Hubbard interaction and at varying interaction strengths. For the free theory, edge entanglement acts as an order parameter, which is supported by analytic calculations and numerical (DMRG) studies. We calculate the symmetry-resolved entanglement and demonstrate the equipartition of entanglement for this model which itself acts as an order parameter when calculated for the edge modes. As the DMRG calculation allows one to go beyond the free theory, we study the entanglement structure of the edge modes in the presence of on-site Hubbard interaction for the same model. A sudden reduction of edge entanglement is obtained as interaction is switched on. The explanation for this lies in the change in the size of the degenerate subspaces in the presence and absence of interaction. We also study the signature of entanglement when the interaction strength becomes extremely strong and demonstrate that the edge entanglement remains protected. In this limit, the energy eigenstates essentially become a tensor product state, implying zero entanglement. However, a remnant entropy survives in the non-trivial topological phase which is exactly due to the entanglement of the edge modes.

cond-mat.str-el↗

arXiv2023

One-Loop Quantum Effects in Carroll Scalars

Carrollian field theories at the classical level possess an infinite number of space-time symmetries, namely the supertranslations. In this article, we inquire whether these symmetries for interacting Carrollian scalar field theory survive in the presence of quantum effects. For interactions polynomial in the field, the answer is in the affirmative. We also study a renormalization group flow particularly tailored to respect the manifest Carroll invariance and analyze the consequences of introducing Carroll-breaking deformations. The renormalization group flow, with perturbative loop-level effects taken into account, indicates a new fixed point apart from the Gaussian ones.

hep-th↗

arXiv2022

Topological Phases in Coupled Polyyne Chains

We study the electronic properties of coupled parallel Polyyne chains in a couple of symmetric stacking arrangements, namely the AA stacking and the stacking AB, with the single and triple carbon bonds of one chain aligned (AA) and anti-aligned (AB) with those of the other chain. Both these arrangements described by tight binding Hamiltonians, whose parameters are calibrated by matching low energy dispersion provided by first principle calculations, fall in the BDI class of topological classification scheme. We calculate the topological invariants for all the three topological phases of the system: one for the AA stacking and 2 for the AB one. In the AA stacking, both the insulating and the metallic phase belongs to the same topological phase. Whereas, the model exhibits two different values of the topological invariant in the two different insulating phases (structurally differentiated by transverse strain). In this later stacking though transition between two distinct topological phases with the closure of the gap is practically unachievable due requirement of high amount of transverse strain. We also show existence of 4 non-zero energy edge modes in the AA stacking and that of 2 zero energy edge modes in one of the topological phases for the AB stacking.

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arXiv2022

Magic Fermions: Carroll and Flat Bands

The Carroll algebra is constructed as the $c\to0$ limit of the Poincare algebra and is associated to symmetries on generic null surfaces. In this paper, we begin investigations of Carrollian fermions or fermions defined on generic null surfaces. Due to the availability of two different (degenerate) metrics on Carroll spacetimes, there is the possibility of two different versions of Carroll Clifford algebras. We consider both possibilities and construct explicit representations of Carrollian gamma matrices and show how to build higher spacetime dimensional representations out of lower ones. Actions for Carroll fermions are constructed with these gamma matrices and the properties of these actions are investigated. We show that in condensed matter systems where the dispersion relation becomes trivial i.e. the energy is not dependent on momentum and bands flatten out, Carroll symmetry generically appears. We give explicit examples of this including that of twisted bi-layer graphene, where superconductivity appears at so called magic angles and connect this to Carroll fermions.

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arXiv2022

Light transformed gluon correlators in CCFT

In the present work, we study celestial correlators of light transformed gluon operators at tree level. We also discuss the transformation of light transformed operators under the action of 4D translations. The two, three and four-point functions arising from MHV amplitudes in terms of light transformed operators satisfy translation invariance constraints, are non-distributional and contain ordinary CFT power law terms. There is a new channel dependent term in the three point function. We show that the three-point light transformed correlation function is conformally covariant after contributions from all the three channels are added. We also study the OPE limit of the different channels of the three-point function in an attempt to construct a map between the OPE in the Mellin basis and that in the light transformed one.

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arXiv2022

Scattering Amplitudes: Celestial and Carrollian

Recent attempts at the construction of holography for asymptotically flat spacetimes have taken two different routes. Celestial holography, involving a two dimensional (2d) CFT dual to 4d Minkowski spacetime, has generated novel results in asymptotic symmetry and scattering amplitudes. A different formulation, using Carrollian CFTs, has been principally used to provide some evidence for flat holography in lower dimensions. Understanding of flatspace scattering has been lacking in the Carroll framework. In this work, using ideas from Celestial holography, we show that 3d Carrollian CFTs living on the null boundary of 4d flatspace can potentially compute bulk scattering amplitudes. 3d Carrollian conformal correlators have two different branches, one depending on the null time direction and one independent of it. We propose that it is the time-dependent branch that is related to bulk scattering. We construct an explicit field theoretic example of a free massless Carrollian scalar that realises some desired properties.

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arXiv2022

Structural Deformation and Metal-Semiconductor Transition in Coupled Carbon Chains

The transition between gapped (semiconducting) and gapless (metallic) phases and tunability of bandgap in materials is a very lucrative yet considerably challenging goal for new-age device preparation. For bulk materials and for two-dimensional layered systems, this is a rapidly expanding field. We theoretically propose a one-dimensional pure carbon material with a tunable bandgap. We find that two parallel coupled polyyne chains show metallic behaviour with bands crossing on the Fermi level, unlike the single semiconducting chain. The number of nodal points (two) is robust under transverse and longitudinal strain, indicating the symmetry-protected nature of the metallic phase. Sliding one chain with respect to the other breaks reflection symmetry and a clear bandgap opens up at the nodes, leading to a gapped phase. By varying the slide parameter, the bandgap can be tuned efficiently. This work initiates and indicates possible topological phases of real one-dimensional materials without the involvement of edge modes.

cond-mat.str-el↗

arXiv2022

Galilean Gauge Theories from Null Reductions

The procedure of null reduction provides a concrete way of constructing field theories with Galilean invariance. We use this to examine Galilean gauge theories, viz. Galilean electrodynamics and Yang-Mills theories in spacetime dimensions 3 and 4. Different non-relativistic conformal symmetries arise in these contexts: Schr{\"o}dinger symmetry in $d=3$ and Galilean conformal symmetry in $d=4$. A canonical analysis further reveals that the symmetries enhance to their infinite dimensional versions in phase space and pick up central extensions. In addition, for the Abelian theory, we discuss non-relativistic electro-magnetic duality in $d=3$ and its difference with the $d=4$ version. We also mention some quantum aspects for both Abelian and non-Abelian theories.

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arXiv2021

Interacting Conformal Carrollian Theories: Cues from Electrodynamics

We construct the free Lagrangian of the magnetic sector of Carrollian electrodynamics. The construction relies on Helmholtz integrability condition for differential equations in a self consistent algorithm, working hand in hand with imposing invariance under infinite dimensional Conformal Carroll algebra. It requires inclusion of new fields in the dynamics and the system is free of gauge redundancies. We next add interaction (quartic) terms to the free Lagrangian, strictly constrained by conformal invariance and Carrollian symmetry. The dynamical realization of the non-semi simple infinite dimensional symmetry algebra at the level of charge algebra is exact and free from central terms.

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arXiv2020

Supersymmetric Localization on dS: Sum over topologies

We find the exact quantum gravity partition function on the static patch of 3d de Sitter spacetime. We have worked in the Chern Simons Formulation of 3d Gravity. To obtain a non-perturbative result, we supersymmetrized the Chern Simons action and used the technique of supersymmetric localization. We have obtained an exact non-perturbative result for the spin-2 gravity case. We comment on the divergences present in the theory. We also comment on higher spin gravity theories and analyse the nature of divergences present in such theories.

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arXiv2020

Field Theories on Null Manifolds

We argue that generic field theories defined on null manifolds should have an emergent BMS or conformal Carrollian structure. We then focus on a simple interacting conformal Carrollian theory, viz. Carrollian scalar electrodynamics. We look at weak (on-shell) and strong invariance (off-shell) of its equations of motion under conformal Carrollian symmetries. Helmholtz conditions are necessary and sufficient conditions for a set of equations to arise from a Lagrangian. We investigate whether the equations of motion of Carrollian scalar electrodynamics satisfy these conditions. Then we proposed an action for the electric sector of the theory. This action is the first example for an interacting conformal Carrollian Field Theory. The proposed action respects the finite and infinite conformal Carrollian symmetries in d = 4. We calculate conserved charges corresponding to these finite and infinite symmetries and then rewrite the conserved charges in terms of the canonical variables. We finally compute the Poisson brackets for these charges and confirm that infinite Carrollian conformal algebra is satisfied at the level of charges.

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arXiv2019

Uniqueness of Galilean Conformal Electrodynamics and its Dynamical Structure

We investigate the existence of action for both the electric and magnetic sectors of Galilean Electrodynamics using Helmholtz conditions. We prove the existence of unique action in magnetic limit with the addition of a scalar field in the system. The check also implies the non existence of action in the electric sector of Galilean electrodynamics. Dirac constraint analysis of the theory reveals that there are no local degrees of freedom in the system. Further, the theory enjoys a reduced but an infinite dimensional subalgebra of Galilean conformal symmetry algebra as global symmetries. The full Galilean conformal algebra however is realized as canonical symmetries on the phase space. The corresponding algebra of Hamilton functions acquire a state dependent central charge.

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