Chartng the  landscape of many-body phenomena

My research interests lie broadly in the physics of quantum and classical many-body systems with an emphasis on the effects due to the presence of rigid structures such as global symmetries. The questions that motivate my work in the long term are:

1. What are the rules governing equilibrium phase diagrams? In other words, how are various types of phases and critical phenomena classified and how are they woven together to form the space of theories? 

2. Can we classify degrees of ergodicity? How can we systematically understand quantum and classical systems that do not satisfy the ergodic hypothesis and thus do not equilibriate in conventional ways? 

3. Can we classify various patterns of quantum entanglement? Which of these can appear as ground states of physical systems? Which can be used for quantum information processing?

Although my main expertise is in condensed matter and statistical physics, I benefit from tools and thinking styles borrowed from certain areas of of high-energy theory, quantum information theory and mathematics  in conjunction with standard tools of many-body physics. 

Below, I summarize various topics I have worked on. The ones at the top are what I am most actively thinking about. All my papers can be found on arXiv here

Although phase diagrams have been the central object of study by the condensed matter and statistical physics community, the connection between phases, critical surfaces and universality classes is surprisingly nebulous and largely driven by dogma. Some of my work in this direction are

• In [1], Sid Parameswaran, Michele Fava, I constructed microscopic models exhibiting 'multiversality' wherein a single critical surface between distinct phases exhibited multiple universality classes and 'unnecessary criticality' wherein a stable second-order critical surface abruptly terminates akin to the liquid-gas transition. These phenomena, first predicted by Senthil and Bi, disprove two widely-held beliefs (i) the universality class of a continuous transition is uniquely fixed by the straddling phases and (ii) stable second-order critical surfaces represent genuine phase transitions and cannot abruptly terminate.

• In [2], Nick Jones and I showed that direct Landau-incompatible transitions between spontaneous symmetry breaking phases can occur in classical statistical mechanical systems introduced about half a century ago. These transitions were earlier dubbed 'deconfined quantum criticality' (DQC) since it was believed that quantum mechanics plays an important role (eg: see this review and this blog). Also thought to be important for DQC are anomalies such as those arising through Lieb-Schultz-Mattis constraints. We show that none of these conditions are necessary and all DQC phenomena, such as the appearance of enhanced symmetry and proliferation of charged defects, can be understood within classical statistical mechanics. We also show that a different class of classical statistical mechanical models can also exhibit unnecessary criticality. These are, to the best of our knowledge, the first examples of unnecessary criticality in classical systems.  

[1] Phys. Rev. Lett. 130, 256401 (Editors' suggestion)
[2] arXiv:2404.19009 [cond-mat.stat-mech]

• In [1], Sid Parameswaran and I show that unnecessary criticality is a consequence of the surrounding family of gapped states forming a topologically non-trivial family i.e. a charge pump. In the language of Hsin, Kapustin and Thorngren, unnecessary critical surfaces are diabolical loci. We also prove a conjecture made in [1] that unnecessary criticality is always accompanied by boundary transitions which 'complete' the unnecessary critical line. This, we show, is a consequence of a a novel anomaly in the space of coupling constants. 

• In [2], with Nick Jones, I show that certain classical statistical mechanical models exhibit unnecessary criticality stabilized by topologically non-trivial families. The nature of these classical non-trivial topological families is being investigated.

[1] arXiv:2408.15351 [cond-mat.str-el]
[2] arXiv:2404.19009 [cond-mat.stat-mech]

Fractons are the name given to excitations which have restricted mobility. These strange systems seem to resist commonly used tools of descriptions such as field theory and have served well as a toy model to understand foundational concepts of physics. The simplest setting they can be found is in the presence of symmetries that conserve multipole moments of charge distribution. My work on fractons is summarized below

• In [1], Shivaji Sondhi, Alain Goriely and I initiated the study of classical fractons i.e. particles conserving dipole moments. We find that the system is 'Machian' where isolated particles are immobile (as expected of fractons) and motion is only possible in the presence of multiple particles. These particles also exhibit dissipative-like dynamics despite conserving energy, seemingly violate Liouville's theorem despite being Hamiltonian systems and are characterized by emergent conservation laws. We also find an exactly solvable limit which confirms these observaitions.

• In [2], Shivaji Sondhi, Ylias Sadki and I study the many-body version of systems introduced in [1]. We find that the many-body system exhibits non-equilibrium steady states that break ergodicity in a way that seems to fall outside the description of statistical mechanics and its theorems. Strikingly, these states spontaneously break translation symmetry in any dimensions forming 'Machian crystals' (see this video made by Ylias) in violation of the Hohenberg-Mermin-Wagner-Coleman theorem. Altogether, fractons seem to represent a new paradigm for non-equilibrium physics.

• In [3],  Shivaji Sondhi, Ylias Sadki, Aryaman Babbar and I show that the formation of Machian crystal formation [1] is accompanied by partial, local chaos although ergodicity is broken globally. We also show that the dynamics generically produces a 'Janus point' (a concept popularized by Julian Barbour) of low complexity and an associated bi-directional arrow of time.  

• In [4] , Shivaji Sondhi, Ylias Sadki, Dan Arovas and I  present a generalization of position-space multipole symmetries to those of phase-space. We classify all symmetry algebras and show that many of them are unbounded leading to only non-trivial dynamics. Among the ones that are bounded, we study a particularly interesting 'self-dual' symmetry case and find a new variety of ergodicity-breaking fracton behaviour not found in [1]-[3]. 

• In [5], Jonathan Classen-Howes, Riccardo Senese and I study quantum dipole conserving fractons on a lattice. We present several rigorous results including the presence of a universal phase diagram consisting of a transition between strong and weak Hilbert-space fragmentation. We introduce several conseptual devices to characterize such systems including 'bottlenecks' through which  transport cannot occur leading to fragmentation. 
  
  

[1] Phys. Rev. B 109, 054313
[2] Phys. Rev. B 110, 024305
[3] arXiv:2501.12445 [cond-mat.stat-mech]
[4] arXiv:2502.02650 [cond-mat.stat-mech]
[5] arXiv:2408.10321 [cond-mat.str-el]

The classification of gapped phases has made great progress. This is because the condition of the spectral gap allows analytical control and the use of powerful tools. Gapless phases on the other hand are harder to classify. In certain cases, for example, when the gapless phase is described by a conformal field theory, some progress can be made. In [1], my collaborators and I show how Luttinger liquids, described by the compact boson  CFT, can be enriched by symmetries in distinct ways, leading to distinct gapless phases of matter which cannot be connected without encountering a phase transition (when the universality class jumps) or an intervening phase. Using a concrete spin ladder model, we show how a myriad of such phases can be present, labelled XY0, XY1, XY2, XY*1, XY*2. Of these, XY*2 is particularly interesting since it hosts topological edge modes despite being gapless!

[1] Phys. Rev. B 108, 245135 (Editors' suggestion)