THEORETICAL CONDENSED MATTER · QUANTUM THEORY
I develop theories connecting quantum geometry to electronic transport, quantum entanglement, and the emergent phases of strongly interacting matter in materials relevant to topological quantum computing.
Principal Investigator on 3 research grantsAlexander Kruchkov
Associate Research Scholar · Princeton University
Moiré materials feature nontrivial quantum geometry and emergent quantum behavior.
Exact identities separate the redistribution of electronic occupation caused by a deforming Fermi surface from changes at fixed momentum, clarifying the role of Luttinger’s constraint.
Read the preprint01 / SELECTED WORK
Contributions to interacting quantum matter, quantum geometry, quantum entanglement, and magic-angle graphene.
arXiv:2610.08921 · October 2026
Exact identities separate the redistribution of electronic occupation caused by a deforming Fermi surface from changes at fixed momentum, clarifying the role of Luttinger’s constraint.
Physical Review B 111, L241111
With Shinsei Ryu, relates the quantum metric to spatial entanglement and Chern-number bounds in gapped two-dimensional lattice systems within a Slater-determinant description.
Physical Review B 107, L241102
Identifies geometric contributions to transport when band velocity vanishes, including a characteristic thermopower scale in a topological flat-band model.
Physical Review Letters 122, 106405
Introduces the Tarnopolsky–Kruchkov–Vishwanath chiral model, now a widely used theoretical framework for magic-angle graphene and correlated flat-band physics. Within this model, vanishing Dirac velocity implies an exactly flat band, revealing analytical structure behind the magic angles.
02 / GRANTS & LEADERSHIP
I lead funded research on quantum materials, topological quantum computation, and quantum geometry, including collaborations with Titus Neupert and Vincent Fortuin.
Swiss National Science Foundation
With Titus Neupert. Project partner: Shinsei Ryu.
View funded projectBranco Weiss Society in Science
With Vincent Fortuin.
View collaborative programGerman Research Foundation (DFG)
Project begins in 2027.
WORKSHOP CO-ORGANIZER
December 4–6, 2024
Princeton Center for Theoretical Science · 407 Jadwin Hall · Princeton University
Workshop announcement & program
OrganizersDuncan Haldane, Alexander Kruchkov, Biao Lian, Shinsei Ryu, and Pok Man Tam
Abstract
The workshop connected quantum geometry with measurable properties of quantum matter and methods for experimental testing. It brought theory and experiment into conversation across unconventional superconductivity, fractional quantum Hall and Chern phases, topological flat bands, and moiré systems. Further themes included solid-state and cold-atom measurements, geometry in nonequilibrium settings, and connections to quantum information and mathematical physics.
Summary of the PCTS workshop announcement.
03 / RESEARCH
How do the hidden geometric properties of quantum states shape the physics we can measure? My work connects this question to materials, entanglement, and strongly interacting systems.
I derive geometric contributions to electrical and thermoelectric transport in topological flat bands, and connect band flatness to Wannier-orbital structure.
With Shinsei Ryu, I relate spatial entanglement bounds to the quantum metric in gapped band systems. This informs my broader program on topological phases for quantum information.
With collaborators, I derive identities for interacting Fermi surfaces and develop transport probes of strong correlations, including Sachdev–Ye–Kitaev physics in disordered graphene.
RESEARCH DIRECTION
My research program asks how quantum geometry and interactions can help predict and control correlated topological phases, including fractional Chern insulators and candidate platforms for topological quantum computing.
As Principal Investigator, I connect quantum-materials theory with computational searches for anyonic phases through projects with Titus Neupert and Vincent Fortuin. My DFG project, beginning in 2027, extends this program across quantum matter and quantum information.
Related funded projects04 / TEACHING
At EPFL, I taught a doctoral course connecting the physical assumptions of moiré models to their mathematical structure.
In Lectures on twisted bilayer graphene (PHYS-756), I connected continuum models and magic angles to band topology, quantum geometry, Wannier functions, and correlated phases. The course was designed for theorists and experimentalists.
The format combined 21 hours of lectures with 7 hours of exercises, giving students space to work through the theory.
Contact me about teaching materialsEPFL · PHYS-756 · DOCTORAL COURSE
From moiré band structures to correlated quantum phenomena, designed for theorists and experimentalists.
View course description
Alexander Kruchkov
05 / ABOUT
I am an Associate Research Scholar in the Department of Physics at Princeton University. My work spans geometric theories of flat bands, entanglement bounds, and transport in strongly interacting electron systems.
I lead an independent research program on the geometric principles of quantum matter, from analytical theories of flat bands to computational searches for anyonic phases. I am Principal Investigator on three research grants connecting quantum materials, quantum geometry, and topological quantum computation.
CV & CONTACT
For faculty search inquiries, research collaborations, and teaching inquiries.
alexkruchkov@princeton.eduDepartment of Physics
Princeton University