Quantum Criticality: Gauge Fields and Matter

May 16, 2022, 8:30 a.m. → May 20, 2022, 5:00 p.m. America/Toronto

Emilie Huffman (Perimeter Institute), Ribhu Kaul (University of Kentucky), Roger Melko (Perimeter Institute & University of Waterloo), Shailesh Chandrasekharan (Duke University)

Ever more efficient numerical methods, such as quantum Monte Carlo sampling of an expanded classes of known sign-problem-free models and tensor network methods have enabled unbiased studies of a number of exotic phases and continuous phase transitions, such as those involving topological phases and emergent gauge fields. The phenomena of interest often arise in simple looking "designer" models, which have appeal to a wide variety of theorists, including those who study condensed matter, high energy physics, and quantum information. The common thread is that these models can be viewed as interesting models of materials, as regularizations of strongly coupled quantum field theories or as playgrounds to study highly entangled quantum systems. This interdisciplinary workshop aims to bring together researchers with the goal of facilitating an exchange of ideas for understanding these models using diverse numerical methods and from the field theoretic point of view.

PIRSA:  https://pirsa.org/C22009

Perimeter Institute will make every effort to host this workshop as an in-person event.  However, we reserve the right to change to an online program to align with changes in regulations due to the COVID-19 pandemic

Territorial Land Acknowledgement

Perimeter Institute acknowledges that it is situated on the traditional territory of the Anishinaabe, Haudenosaunee, and Neutral peoples.

Perimeter Institute is located on the Haldimand Tract. After the American Revolution, the tract was granted by the British to the Six Nations of the Grand River and the Mississaugas of the Credit First Nation as compensation for their role in the war and for the loss of their traditional lands in upstate New York. Of the 950,000 acres granted to the Haudenosaunee, less than 5 percent remains Six Nations land. Only 6,100 acres remain Mississaugas of the Credit land.

We thank the Anishinaabe, Haudenosaunee, and Neutral peoples for hosting us on their land.

Monday, May 16

8:30 a.m. Registration

1 Welcome and Opening Remarks

Speakers: Emilie Huffman (Perimeter Institute), Ribhu Kaul (University of Kentucky), Roger Melko (Perimeter Institute & University of Waterloo), Shailesh Chandrasekharan (Duke University)

2 Blackboard Talk 1 - Virtual

Speaker: Senthil Todadri (Massachusetts Institute of Technology)

10:00 a.m. Coffee Break

3 Blackboard Talk 2 - Virtual

Speaker: Senthil Todadri (Massachusetts Institute of Technology)

11:15 a.m. Break

12:30 p.m. Lunch

4 Research Talk

Speaker: Fakher Assaad (University of Wuerzburg)

2:45 p.m. Break

5 Reducing the Sign Problem with Complex Neural Networks

The sign problem is arguably the greatest weakness of the otherwise highly efficient, non-perturbative Monte Carlo simulations. Recently, considerable progress has been made in alleviating the sign problem by deforming the integration contour of the path integral into the complex plane and applying machine learning to find near-optimal alternative contours. This deformation however requires a Jacobian determinant calculation which has a generic computational cost scaling as volume cubed. In this talk I am going to present a new architecture with linear runtime, based on complex-valued affine coupling layers.

Speaker: Johann Ostmeyer (University of Liverpool)

3:45 p.m. Coffee Break

6 Self dual U(1) lattice field theory with a theta-term

Starting from the Villain formulation with an additional constraint we construct a self-dual lattice version of U(1) field theory with a theta-term. An interesting feature is that the self-dual symmetry gives rise to an action that is local but not ultra-local, similar to lattice actions that implement chiral symmetry. We outline how electric and magnetic matter can be coupled in a self-dual way and discuss the emerging symmetry structure with the theta term. We present results from a Monte Carlo simulation of the self-dual system with electric and magnetic matter and explore spontaneous breaking of the self-dual symmetry.

Speaker: Christoff Gattringer (Austrian Science Fund)

5:00 p.m. Break

Moderated Discussion

Tuesday, May 17

7 Quantum electrodynamics with massless fermions in three dimensions - Talk 1

Speaker: Rajamani Narayanan (Florida International University)

9:45 a.m. Coffee Break

8 Quantum electrodynamics with massless fermions in three dimensions - Talk 2

Speaker: Rajamani Narayanan (Florida International University)

11:00 a.m. Break

12:30 p.m. Lunch

9 New topological phases in the Kitaev model as a function of magnetic field

"The Kitaev model with anisotropic interactions on the bonds of a honeycomb lattice is a paradigmatic model for quantum spin liquids. Despite the simplicity of the model, a rich phase diagram with gapless and gapped quantum spin liquid phases, with abelian and non-abelian excitations, are revealed as a function of a magnetic field and bond couplings. Our results of the entanglement entropy, topological entanglement entropy, and the dynamical spin excitation spectrum, are obtained using exact diagonalization and density matrix renormalization group (DMRG) methods. We provide insights into the phases from the underlying effective field theories.

In collaboration with Shi Feng, Cullen Gantenberg, Adhip Agarwala, Subhro Bhattacharjee

[1] Signatures of magnetic-field-driven quantum phase transitions in the entanglement entropy and spin dynamics of the Kitaev honeycomb model, David C. Ronquillo, Adu Vengal, Nandini Trivedi, Phys. Rev. B 99, 140413 (2019)

[2] Magnetic field induced intermediate quantum spin-liquid with a spinon Fermi surface, Niravkumar D. Patel and Nandini Trivedi, Proceedings of the National Academy of Sciences 116, 12199 (2019).

[3] Two-Magnon Bound States in the Kitaev Model in a [111]-Field, Subhasree Pradhan, Niravkumar D. Patel, Nandini Trivedi, Phys. Rev. B 101, 180401 (2020)

[4] Symmetry Analysis of Tensors in the Honeycomb Lattice of Edge-Sharing Octahedra, Franz G. Utermohlen, Nandini Trivedi, Phys. Rev. B 103, 155124 (2021) "

Speaker: Nandini Trivedi (Ohio State University)

2:45 p.m. Coffee Break

10 Deconfined multi-criticality in quantum spin models and experiments

In the original field theoretical scenario of deconfined quantum criticality, the deconfined quantum-critical point (DQCP) separating antiferromagnetic (AFM) and singlet-solid phases of quantum magnets is generic, i.e., does not require fine-tuning. Recent numerical studies instead point to a fine-tuned multi-critical DQCP [1] that is also the end-point of a gapless spin liquid phase [2]. An example is the Shastry-Sutherland (SS) model, where a narrow spin liquid phase was recently detected [2,3], instead of the previously argued direct transition between plaquette singlet solid (PSS) and AFM phases. The multi-critical DQCP, followed by a direct transition without intervening spin liquid, can be reached when other interactions are included. Very recent NMR experiments on the SS compound SrCu2(BO3)2 under high pressures and high magnetic fields are consistent with this scenario [4]. Low-temperature (below 0.1 K) direct PSS to XY-AFM transitions were observed that become less strongly first-order at higher pressures. At the highest pressure, quantum-critical scaling of the spin-lattice relaxation was observed, indicating close proximity to a DQCP. This point may be the end-point of a not yet confirmed quantum spin liquid phase existing at slightly higher pressures.

[1] B. Zhao, J. Takahashi, and A. W. Sandvik, PRL 125, 257204 (2020).
[2] J. Yang, A. W. Sandvik, and L. Wang, PRB 105, L060409 (2022).
[3] L. Wang, Y. Zhang, and A. W. Sandvik, arXiv:2205.02476
[4] Y. Cui et al., arXiv:2204.08133.

Speaker: Anders Sandvik (Boston University)

4:00 p.m. Wine & Cheese Reception

Wednesday, May 18

11 A Sport and a Pastime: Model design and computation for quantum criticality, gauge fields and matter

Speaker: Zi Yang Meng (University of Hong Kong)

9:45 a.m. Coffee Break

12 Dirac criticality from field theory beyond the leading order

Two-dimensional gapless Dirac fermions emerge in various condensed-matter settings. In the presence of interactions such Dirac systems feature critical points and the precision determination of their exponents is a prime challenge for quantum many-body methods. In a field-theoretical language, these critical points can be described by Gross-Neveu-Yukawa-type models and in my talk I will show some results on Gross-Neveu critical behavior using field theoretical approaches beyond the leading order. To that end, I will first present higher-loop perturbative RG calculations for generic Gross-Neveu-Yukawa models and compare estimates for the exponents with recent corresponding results from Quantum Monte Carlo simulations and the conformal bootstrap. Then, I will discuss a more exotic variant of Gross-Neveu-Yukawa models which describes the interacting fractionalized excitations of two-dimensional frustrated spin-orbital magnets. Here, we have provided field-theoretical estimates for the critical exponents employing higher-order epsilon expansion, large-N calculations, and functional renormalization group.

Speaker: Michael Scherer (Ruhr University Bochum )

11:00 a.m. Break

13 Probing sign structure using measurement-induced entanglement

The sign structure of quantum states is closely connected to quantum phases of matter, yet detecting such fine-grained properties of amplitudes is subtle. We employ as a diagnostic measurement-induced entanglement (MIE)-- the average entanglement generated between two parties after measuring the rest of the system. We propose that for a sign-free state, the MIE upon measuring in the sign-free basis decays no slower than correlations in the state before measurement. Concretely, we prove that MIE is upper bounded by mutual information for sign-free stabilizer states (essentially CSS codes), which establishes a bound between scaling dimensions of conformal field theories describing measurement-induced critical points in stabilizer systems. We also show that for sign-free qubit wavefunctions, MIE between two qubits is upper bounded by a simple two-point correlation function, and we verify our proposal in several critical ground states of one-dimensional systems, including the transverse field and tri-critical Ising models. In contrast, for states with sign structure, such bounds can be violated, as we illustrate in critical hybrid circuits involving both Haar or Clifford random unitaries and measurements, and gapless symmetry-protected topological states.

Speaker: Tim Hsieh (Perimeter Institute)

12:00 p.m. Break

12:30 p.m. Lunch

14 Quantum steampunk: Quantum information meets thermodynamics

Thermodynamics has shed light on engines, efficiency, and time’s arrow since the Industrial Revolution. But the steam engines that powered the Industrial Revolution were large and classical. Much of today’s technology and experiments are small-scale, quantum, far from equilibrium, and processing information. Nineteenth-century thermodynamics needs re-envisioning for the 21st century. Guidance has come from the mathematical toolkit of quantum information theory. Applying quantum information theory to thermodynamics sheds light on fundamental questions (e.g., how does entanglement spread during quantum thermalization? How can we distinguish quantum heat from quantum work?) and practicalities (e.g., quantum engines and the thermodynamic value of coherences). I will overview how quantum information theory is being used to revolutionize thermodynamics in quantum steampunk, named for the steampunk genre of literature, art, and cinema that juxtaposes futuristic technologies with 19th-century settings.

Speaker: Nicole Yunger Halpern (University of Maryland)

3:00 p.m. Colloquium Reception

15 Superconductivity, charge density wave, and supersolidity in flat bands with tunable quantum metric

Predicting the fate of an interacting system in the limit where the electronic bandwidth is quenched is often highly non-trivial. The complex interplay between interactions and quantum fluctuations driven by the band geometry can drive a competition between various ground states, such as charge density wave order and superconductivity. In this work, we study an electronic model of topologically-trivial flat bands with a continuously tunable Fubini-Study metric in the presence of on-site attraction and nearest-neighbor repulsion, using numerically exact quantum Monte Carlo simulations. By varying the electron filling and the spatial extent of the localized flat-band Wannier wavefunctions, we obtain a number of intertwined orders. These include a phase with coexisting charge density wave order and superconductivity, i.e., a supersolid. In spite of the non-perturbative nature of the problem, we identify an analytically tractable limit associated with a `small' spatial extent of the Wannier functions, and derive a low-energy effective Hamiltonian that can well describe our numerical results.

Speaker: Johannes Hofmann (Weizmann Institute of Science)

4:15 p.m. Break

16 Neural annealing and visualization of autoregressive neural networks

Artificial neural networks have been widely adopted as ansatzes to study classical and quantum systems. However, some notably hard systems such as those exhibiting glassiness and frustration have mainly achieved unsatisfactory results despite their representational power and entanglement content, thus, suggesting a potential conservation of computational complexity in the learning process. We explore this possibility by implementing the neural annealing method with autoregressive neural networks on a model that exhibits glassy and fractal dynamics: the two-dimensional Newman-Moore model on a triangular lattice. We find that the annealing dynamics is globally unstable because of highly chaotic loss landscapes. Furthermore, even when the correct ground state energy is found, the neural network generally cannot find degenerate ground-state configurations due to mode collapse. These findings indicate that the glassy dynamics exhibited by the Newman-Moore model caused by the presence of fracton excitations in the configurational space likely manifests itself through trainability issues and mode collapse in the optimization landscape.

Speaker: Estelle Inack (Perimeter Institute)

5:15 p.m. Break

17 Data-enhanced variational Monte Carlo for Rydberg atom arrays

Rydberg atom arrays are programmable quantum simulators capable of preparing interacting qubit systems in a variety of quantum states. However, long experimental state preparation times limit the amount of measurement data that can be generated at reasonable timescales, posing a challenge for the reconstruction and characterization of quantum states. Over the last years, neural networks have been explored as a powerful and systematically tuneable ansatz to represent quantum wavefunctions. These models can be efficiently trained from projective measurement data or through Hamiltonian-guided variational Monte Carlo. In this talk, I will compare the data-driven and Hamiltonian-driven training procedures to reconstruct ground states of two-dimensional Rydberg atom arrays. I will discuss the limitations of both approaches and demonstrate how pretraining on a small amount of measurement data can significantly reduce the convergence time for a subsequent variational optimization of the wavefunction.

Speaker: Stefanie Czischek (Perimeter Institute & University of Waterloo)

18 A minimalist's approach to the physics of emergence

One of the central themes of quantum many-body physics and quantum field theory is the emergence of universality classes. In general, determining which universality class emerges in a quantum many-body system is a highly complex problem. I will argue that the perspective of quantum anomaly provides powerful insights to the understanding of the landscape of universality classes that can emerge in a quantum matter, and I will present some interesting applications.

Speaker: Liujun Zou (Perimeter Institute)

Thursday, May 19

19 Emergibility: from lattice spins to critical gauge theories and beyond - Talk 1

Speaker: Chong Wang (Perimeter Institute)

9:45 a.m. Coffee Break

20 Emergibility: from lattice spins to critical gauge theories and beyond - Talk 2

Speaker: Chong Wang (Perimeter Institute)

11:00 a.m. Break

12:30 p.m. Lunch

21 Multiband superconductivity and the breaking of time reversal symmetry

I will discuss how spontaneous breaking of time reversal symmetry in multiband superconductors leads quite generally to the formation of small Fermi surfaces of Bogoliubov excitations, irrespective of whether inversion symmetry is absent or present in the superconducting state. In the latter case the inversion symmetry is susceptible to being dynamical broken at low temperatures by the residual interactions. A lattice model of this process will be discussed. Its final result is a reduced, but still finite Bogoliubov-Fermi surface.

Speaker: Igor Herbut (Simon Fraser University)

2:45 p.m. Coffee Break

22 Bootstrapping critical gauge theories

I will talk about our recent progress on bootstrapping critical gauge theories. In specific, I will first introduce the current understanding that why bootstrap works, for example, why a CFT can sit at a kink of bootstrap bounds and why CFT can be isolated as an island. Then, I will apply these idea to a prototypical critical gauge theory--the scalar QED (i.e. SU(N) deconfined phase transition), and demonstrate it can be isolated in a bootstrap island when the matter flavour is large.

Speaker: Yin-Chen He (Perimeter Institute)

4:00 p.m. Break

23 Fractionalized fermionic quantum criticality

In frustrated magnets, novel phases characterized by fractionalized excitations and emergent gauge fields can occur. A paradigmatic example is given by the Kitaev model of localized spins 1/2 on the honeycomb lattice, which realizes an exactly solvable quantum spin liquid ground state with Majorana fermions as low-energy excitations. I will demonstrate that the Kitaev solution can be generalized to systems with spin and orbital degrees of freedom. The phase diagrams of these Kitaev-Kugel-Khomskii spin-orbital magnets feature a variety of novel phases, including different types of quantum liquids, as well as conventional and unconventional long-range-ordered phases, and interesting phase transitions in between. In particular, I will discuss the example of a continuous quantum phase transition between a Kitaev spin-orbital liquid and a symmetry-broken phase. This transition can be understood as a realization of a fractionalized fermionic quantum critical point.

Speaker: Lukas Janssen (Technical University Dresden)

5:00 p.m. Break

Moderated Discussion

Friday, May 20

24 Anomalies and symmetric mass generation for staggered fermions – Talk 1

Speaker: Simon Catterall (Syracuse University)

9:45 a.m. Coffee Break

25 Anomalies and symmetric mass generation for staggered fermions – Talk 2

Speaker: Simon Catterall (Syracuse University)

11:00 a.m. Break

26 Deconfined quantum critical points with emergent SO(5) symmetry in fermionic models

Speaker: Hong Yao (Tsinghua University)

12:00 p.m. Lunch

27 (Multi-)Critical Point, and Potential Realization with infinite Fractal Symmetries

In the last few years the concept of symmetry has been significantly expanded. One exotic example of the generalized symmetries, is the “type-II subsystem symmetry”, where the conserved charge is defined on a fractal sublattice of an ordinary lattice. In this talk we will discuss examples of models with the fractal symmetries. In particular, we will introduce a quantum many-body model with a “Pascal’s triangle symmetry”, which is an infinite series of fractal symmetries, including the better known Sierpinski-triangle fractal symmetry. We will also construct a gapless multicritical point with the Pascal’s triangle symmetry, where the generator of all the fractal symmetries decay with a power-law. If time permits, we will also mention a few potential experimental realizations for models with fractal symmetries.

Speaker: Cenke Xu (University of California, Santa Barbara)

28 Quantum Criticality in the 2+1d Thirring Model

"The Thirring Model is a covariant quantum field theory of interacting fermions, sharing many features in common with effective theories of two-dimensional electronic systems with linear dispersion such as graphene.

For a small number of flavors and sufficiently strong interactions the ground state may be disrupted by condensation of particle- hole pairs leading to a quantum critical point. With no small dimensionless parameters in play in this regime the Thirring model is plausibly the simplest theory of fermions requiring a numerical solution.

I will review what is currently known focussing on recent results and challenges from simulations employing Domain Wall Fermions, a formulation drawn from state-of-the-art lattice QCD, to faithfully capture the underlying symmetries at the critical point."

Speaker: Simon Hands (University of Liverpool)

29 Thank you and Good-Bye

Speakers: Emilie Huffman (Perimeter Institute), Ribhu Kaul (University of Kentucky), Roger Melko (Perimeter Institute & University of Waterloo), Shailesh Chandrasekharan (Duke University)

2:35 p.m. Coffee Break