The full list of our publications is available here.

## Overview of our Research

We engage in theoretical research on various topics in the condensed matter physics of quantum matter, ranging from strongly-correlated electronic systems, quantum magnetism, topological phases of matter, non-Fermi liquids and low-dimensional systems. One of our primary goals is to understand the fascinating and complex phenomenology displayed by many materials studied in the laboratory. But this is no simple task: we seek to understand the quantum physics of a macroscopic number of electrons that are interacting with one another. And their physics appears to lie in a regime where the electronic potential energy (due to electron repulsion) is of the same order as their kinetic energy. In keeping with this, our work has often involved the development of non-perturbative methods (e.g., a novel renormalisation group method based purely on many-particle unitary transformations) and applying them towards understanding some challenging open questions and problems (e.g., the origin of high-temperature superconductivity from electrons that face strongly repulsive interactions).

## Broad areas of research

We focus on the following areas in our research:

- Strongly correlated electron systems,
- Frustrated quantum magnetism,
- Non-Fermi liquids,
- Unconventional superconductivity,
- Topological states of matter and Topological order,
- Fermionic Criticality,
- Many-particle entanglement,
- Low-dimensional quantum systems,
- Quantum transport,
- Search for quantum materials

## Methods we use (and develop)

We employ, as well as develop, analytic and numerical methods to find answers to our questions. This includes

- Variety of renormalisation group (RG) methods to determine quantum phase diagrams (critical, saddle and stable fixed points). We have developed a non-perturbative RG scheme based purely on many-particle unitary transformations that leads to stable fixed points for the evolution of the Hamiltonian and its couplings.
- We have also extended this to obtain the RG evolution of the many-particle entanglement content of the ground state, and low-lying excited states, of interacting fermionic matter.
- Methods by which to identify the appropriate quantum order parameters for topological states of matter. These are composite objects (e.g., Wilson loops) that lead to quantum ordered ground states. They are represented by operators that exploit emergent symmetries and lead to topological quantum dynamics.

## Questions we have worked on

### Strong correlations and exotic superconductivity

Strongly correlated systems often show the proximity of unconventional superconductivity, non-Fermi liquids and insulating magnetic states of quantum matter. Well known examples include the cuprates and heavy fermion systems. We are interested in understanding how the enhanced quantum fluctuations in low-dimensional (e.g., two dimensional) versions of such systems can enhance the emergence of complexity.

**Relevant works**

- Holographic entanglement renormalisation of topological order in a quantum liquid
- Scaling theory for Mott–Hubbard transitions: II. T = 0 phase diagram of the 1/2-filled Hubbard model
- Scaling theory for Mott–Hubbard transitions: I. T = 0 phase diagram of the 1/2-filled Hubbard model

### Topological phases, symmetry breaking and entanglement

Topological states of matter are known to be governed by rules that depart from the traditional Ginzburg-Landau-Wilson paradigm of local order parameters and spontaneous symmetry breaking. The entanglement properties of the many-body Hilbert space are believed to be key to the ongoing search for topological order in quantum matter. We are presently focussed on asking how topological order can arise in correlated fermionic quantum matter.

**Relevant works**

- Graph Polynomial for Colored Embedded Graphs: A Topological Approach
- Unveiling topological order through multipartite entanglement
- Origin of Topological Order in a Cooper Pair Insulator
- Correlated spin liquids in the quantum kagome antiferromagnet at finite field: a renormalisation group analysis

### Fermionic criticality and models of correlated electrons

Quantum criticality associated with correlated electrons likely require order parameters that describe the geometry and topology of the Fermi surface. We are interested in investigating quantum phase transitions that involve drastic changes in the exchange statistics of excitations lying above the ground state and changes in the topology of the Fermi surface (Lifshitz transitions).

**Relevant works**

- Holographic unitary renormalization group for correlated electrons – II: insights on fermionic criticality
- Holographic unitary renormalization group for correlated electrons – I: a tensor network approach
- Fermionic criticality is shaped by Fermi surface topology: a case study of the Tomonaga-Luttinger liquid

### Fustrated magnetism and spin liquids

The study of frustrated magnetism is at the heart of the search for liquid-like states arising in systems of interacting quantum spins. Such states do not display any ordering of the constituent spins even at T=0. Instead, there exist predictions of topological order in some gapped spin liquid states. We are interested in investigating whether such proposals can be realised in geometrically frustrated systems like the Kagome or pyrochlore lattices.

**Relevant works**

- Non-perturbative approach to quantum liquid ground states on geometrically frustrated Heisenberg antiferromagnets
- Orbital and spin ordering physics of the Mn\(_3\)O\(_4\) spinel

### Quantum impurities & auxiliary models

Correlated quantum impurity models serve as fertile grounds for the emergence of various quantum-mechanical properties like entanglement, frustration, non-Fermi liquid physics and quantum phase transitions. They also find use as auxiliary models in methods like dynamical mean-field theory. The rich physics in these models often means that different methods lead to new insights on already-solved problems.

**Relevant works**

- Kondo frustration via charge fluctuations: a route to Mott localisation
- Frustration shapes multi-channel Kondo physics: a star graph perspective
- Unveiling the Kondo cloud: unitary RG study of the Kondo model

### Many-particle entanglement & holography

In the last few decades, quantum entanglement has become very important for studying the nature of quantum condensed matter systems. For instance, gapped interacting many-body systems typically display an area-law scaling of the subsystem entanglement entropy with subsystem size, while quantum critical systems are expected to display a volume law scaling of the same.

**Relevant works**

- Holographic entanglement renormalisation for fermionic quantum matter: geometrical and topological aspects
- Holographic unitary renormalization group for correlated electrons – II: insights on fermionic criticality
- Holographic unitary renormalization group for correlated electrons – I: a tensor network approach
- Fermionic criticality is shaped by Fermi surface topology: a case study of the Tomonaga-Luttinger liquid

### Quantum transport

While transport in quantum systems is a vast field in itself, we are keenly interested in understanding how it is shaped by inter-particle interactions, low-dimensionality and the geometry & topology of the system. Systems of interest include transport on the edge states of 2D topological insulators (e.g., quantum Hall systems, graphene), quantum wires of interacting electrons (described by the 1D Tomonaga-Luttinger liquid), quantum dots of various kinds etc.

### Quantum materials

There are many surprises thrown up by experiments on strongly interacting quantum matter. For instance, the cuprate family of Mott insulators turn superconducting upon doping with holes. Indeed, many such puzzling observations abound in several families of materials. Over the years, EPQM has studied many of them, including the cuprates, organic conductors, perovskites, halides, spinels, insulators with active magnetic moments and orbitals degrees of freedom, materials that are effectively low-dimensional spin systems.

For more information, please visit the about page and the publications page.

## Some of our Codes are open-source

Some of the numerical implementations of our methods, e.g., the unitary Renormalisation Group (URG) and the momentum-space entanglement renormalisation group (MERG) are available on GitHub and Zenodo. Please do share your feedback with us if you use/modify our codes.

## Thanks to our Funders

We are thankful for research funding from SERB and IISER Kolkata for implementing our projects. Also, to CSIR and IISER Kolkata for the research fellowships for several of EPQM’s research scholars. None of this would have been possible but for the honest taxpayers of the Republic of India.