**Time/Venue** Friday, January 8 at 2:00 pm Pacific Time via this Zoom link**Host** Mike Zaletel**Title** Intertwined topological and broken symmetry orders in fractional Chern insulators**Abstract** Recent advances in the engineering of topological band structures in solid-state and cold-atom systems have raised the possibility of realizing fractional Chern insulators (FCIs), lattice analogues of fractional quantum Hall (FQH) states formed in Chern bands. It is thus of experimental interest to understand how the underlying lattice can drive new physics in these states. To that end, we investigate FCI states arising from pairing of composite fermions, analogous to the Moore-Read FQH state, in the square-lattice Hofstadter model. We find that magnetic translation symmetry favors finite-momentum pairing which, as in pair-density wave theories of the cuprates, can lead to concomitant charge-density wave order. These novel paired FCI states are thus characterized by the simultaneous emergence – or intertwining – of topological and broken symmetry orders. We obtain mean-field phase diagrams exhibiting a rich array of these striped topological phases, establishing paired FCI states as ideal platforms to investigate the phenomenon of intertwined orders.

## Special QM Seminar Speaker, Ramanjit Sohal (University of Illinois at Urbana-Champaign) Friday, January 8 at 2:00 pm

## Special QM Seminar Speaker Oles Shtanko (JQI and QuICS, UMD College Park) Friday, December 4 at 2:00 pm

**Time/Venue **Friday, December 4 at 2:00 pm Pacific Time via this Zoom link:https://berkeley.zoom.us/j/93181359950

**Norman Yao**

Host

Host

**Title**Complexity Transitions in Open Many-Body Systems

**Abstract**Under the environment’s action, open quantum many-body systems are often transitioning into a classical regime described by a polynomial number of parameters and simulable by a classical algorithm. Understanding the conditions of this transition is crucial for quantum computing and classifying open quantum phases. In my talk, I will explore this phenomenon using two different measures: computational hardness and quantum entanglement. I will propose free fermions with quadratic jump operators as a promising candidate for the complexity transition. I also show that, under an anticoncentration assumption, the transition in entanglement in monitored random circuits maps to a disordered classical phase transition.

## Special QM Seminar Speaker, Leo Zhou (Harvard) Thursday, December 3 at 4:00 pm

**Time/Venue** Thursday, December 3 at 4:00 pm Pacific Time via this Zoom link**Host** Norman Yao**Title** Quantum Simulation and Optimization in Near-Term Quantum Computers**Abstract**: Quantum simulation and optimization are two of the most promising applications of near-term quantum computers. In fact, there are already many experiments where analog simulations of quantum models are implemented to probe interesting physical phenomena. Some experiments have also begun testing performance of quantum algorithms for optimization.

In this two-part talk, I will first describe our study of the resource required to simulate a quantum Hamiltonian by another whose underlying interaction graph is simpler. We show a surprising result that unlike the classical setting, reducing the graph degree to a constant is impossible in general unless the interaction energy diverges with system size n. Instead, we develop a new construction where such degree-reduction becomes possible using O(poly(n)) interaction energy, which is exponentially better than what was known previously. In the second part, I will discuss our recent insights into the performance and mechanism of a general-purpose Quantum Approximate Optimization Algorithm (QAOA). We develop a parameter-optimization procedure for the QAOA that is exponentially more efficient than standard strategies and reveal a mechanism of the algorithm to exploit non-adiabatic operations. We also analyze the typical-case performance of the QAOA on the Sherrington-Kirkpatrick spin glass problem and find that it can outperform the classical semi-definite programming algorithm. Implementations in experiments are also discussed.**References**:

[1] D. Aharonov and **LZ**, “*Hamiltonian sparsification and gap-simulation,”*arXiv:1804.11084.

[2] **LZ**, S.T. Wang, S. Choi, H. Pichler, and M.D. Lukin, “*Quantum Approximate Optimization Algorithm: Performance, Mechanism, and Implementation on Near-Term Devices,”*arXiv:1812.01041.

[3] E. Farhi, J. Goldstone, S. Gutmann, and **LZ**, “*The Quantum Approximate Optimization Algorithm and the Sherrington-Kirkpatrick Model at Infinite Size,”*arXiv:1910.08187.

## Special QM Seminar Speaker Daniel Ranard (Stanford) Wednesday, December 2 at 10:00 am

**Time/Venue** Wednesday, December 2, at 10:00 am Pacific Time via this Zoom link**Host** Michael Zaletel**Title** Emergent classicality in the dynamics of large systems

Abstract In a quantum measurement process, classical information about the measured system spreads through the environment. In contrast, quantum information about the system becomes inaccessible to local observers. In this talk, I will present a result about quantum channels indicating that an aspect of this phenomenon is completely general. We show that for any evolution of the system and environment, for everywhere in the environment excluding an O(1)-sized region we call the “quantum Markov blanket,” any locally accessible information about the system must be approximately classical, i.e. obtainable from some fixed measurement. The result strengthens the earlier result of arXiv:1310.8640, allowing applications to understanding and simulating many-body systems.

Based on: arXiv:2001.01507 with Xiao-Liang Qi

## Special QM Seminar Speaker, Chunxiao Liu (UCSB) Friday November 20 at 2:00 pm

**Time/Venue** Friday November 20 at 2:00 pm Pacific Time via this Zoom link**Host** Ehud Altman/Joel Moore**Title** Quantum spin liquids on the pyrochlore lattice: symmetry classification, proximate orders, and gauge theories**Abstract** Quantum spin liquids are zero-temperature phases of interacting spin systems which possess intrinsic long-range entanglement and support nonlocal excitations carrying fractionalized quantum numbers. The geometrically frustrated pyrochlore lattice has long been predicted to host a quantum spin ice state, a special type of U(1) spin liquid in three dimensions whose only low energy excitations are emergent photons of Maxwell type. Existing pyrochlore experiments, on the other hand, have discovered several weakly ordered states and a tendency of close competition amongst them. Motivated by these facts, we give a complete classification of spin-orbit-coupled Z2 and U(1) spin-liquid states on the pyrochlore lattice by using the projective symmetry group (PSG) approach for bosonic and fermionic partons. The bosonic PSG allows us to map out phase diagrams that link magnetic orders to specific spin liquids. We find that seemingly unrelated magnetic orders are intertwined with each other and that the conventional spin orders seen in the experiments are accompanied by more exotic hidden orders. The fermionic PSG leads to the discovery of novel classes of U(1) spin liquids that possess an unusual gapless multi-nodal line structure in the spinon bands protected by the projective symmetry of the pyrochlore space group. Through a toy model, we study the effect of gauge fluctuations for such a nodal structure and specify the leading contributions to the low temperature specific heat. Our study provides a clear map and various new types of pyrochlore phases for future experiments and variational Monte Carlo studies in pyrochlore materials.

## Special QM Seminar Speaker Xue-Yang Song (Harvard), Thursday, November 19 at 4:00 pm

**Host** Ehud Altman**Time/Venue** Thursday, November 19 at 4:00 pm Pacific Time via this Zoom link**Talk Title** Dirac spin liquids on the square, kagome and triangular lattices: Unified theory for 2D quantum magnets and doped electronic phases**Abstract** Quantum magnets provide the simplest example of strongly interacting quantum matter, yet they continue to resist a comprehensive understanding above one spatial dimension. We explore the Dirac spin liquid (DSL) on 2D lattices, a version of Quantum Electrodynamics (QED3) with four flavors of Dirac fermions coupled to photons. Importantly, its excitations include magnetic monopoles that drive confinement, and the symmetry actions on monopoles contain crucial information about the DSL states. The underlying band topology of spinon insulators, e.g., wannier insulator protected by rotation etc, determines the elusive Berry phase of monopoles. The stability of the DSL is enhanced on triangular and kagome lattices compared to square(bipartite) lattices. We obtain the universal signatures of the DSL on triangular and kagome lattices, including those of monopole excitations, as a guide to numerics and experiments on existing materials. Even when unstable, the DSL helps unify and organize the plethora of competing orders in correlated two-dimensional materials.

Time permitting I will describe recent results on chiral spin liquid states on the triangular lattice and the superconducting/metallic phases that emerge on lightly doping them.

## Special QM Seminar Speaker Tianci Zhou (UCSB) Wednesday, November 18, 10:00 am Pacific Time

**Host** Ehud Altman**Time/Venue** Wednesday, November 18 at 10:00 am Pacific Time via this Zoom link**Talk Title** The entanglement membrane in chaotic many-body systems**Abstract** In this work, we propose a new universality class for dynamical quantities involving multiple forward and backward evolutions, such as out-of-time-order correlation functions and entanglement entropies. In certain analytically tractable models, the evaluation of these quantities reduces to an effective theory of an “entanglement membrane” by averaging over random local unitaries defining the dynamical evolution. We show here how to make sense of this membrane in more realistic models without randomness. Our approach relies on introducing effective degrees of freedom that pairs the forward and backward trajectories in spacetime, which allows us to carry over the scaling pictures from random unitary circuits to non-random models. We show that a consistent line tension may be defined for the entanglement membrane. And we provide an efficient numerical algorithm to evaluate it in some translationally invariant Floquet spin chains studied in the literature.

## Special QM Seminar Speaker Etienne Lantagne-Hurtubise (UBC) Friday November 13, 2:00 pm Pacific Time

**Host** Ehud Altman**Time/Venue** Friday November 13, 2:00 pm Pacific Time via this Zoom link**Talk Title** Coupled SYK models: black holes, wormholes and superconductors**Abstract** I will summarize our recent explorations of the intriguing physics of coupled SYK models, which were predicted by Maldacena and Qi to harbor a phase of matter dual to an eternal traversable wormhole. I will first discuss the finite-temperature dynamical properties of the Maldacena-Qi model, which exhibits revival oscillations in the transmission of fermions between the two SYK models, and explain their relation to the conformal structure of the model’s excitations. I will then generalize this story to an analogous complex fermion model with a global U(1) symmetry and explore its phase diagram, which turns out to be even richer than its Majorana counterpart. Finally, I will discuss how our results inform proposals for realizations of SYK physics in disordered graphene flakes and, if time permits, give an overview of ongoing work on superconducting instabilities in spinful SYK models with time-reversal symmetry.

## Special QM Seminar Speaker Shang Liu (Harvard) Thursday, November 12, 4:00 pm Pacific Time

**Host** Ehud Altman**Time/Venue** Thursday, November 12, 4:00 pm Pacific Time via this link at Zoom.**Talk Title**: Large-N Approach to Gapless SPT**Abstract: **Significant progress in the study of classical and quantum phase transitions involving symmetry breaking has been achieved over the past decades. Now, a new set of questions have been thrown up by the discovery of symmetry protected topological states (SPTs), that generalize the notion of topological insulators. Here, symmetries and a bulk gap stabilize unusual modes at surfaces or at topological defects. What is the fate of these protected modes at a quantum critical point, when the protecting symmetries are on the verge of being broken? This interplay of topology and criticality is expected to be extremely rich, given that it incorporates both the bulk dynamics of critical points described by nontrivial conformal field theories and the intrinsically quantum aspects of SPT physics. Combining these two disparate ingredients in an analytically tractable framework is challenging. Here, we make progress towards this goal by studying the simplest nontrivial model – that of a 0+1 dimensional topological mode, coupled to a 2+1D critical bulk – using the large-N technique. We introduce a series of models that can be solved within the large-N approximation which, as a consequence of topology, demonstrate intermediate coupling fixed points. We compare our results to previous numerical simulations and find good agreement. We also point out some intriguing connections to the physics of Sachdev-Ye-Kitaev (SYK) models, in particular we show that a Luttinger theorem derived for the complex SYK models, that relates the charge density to particle-hole asymmetry, also holds in our setting. These results should help open up the analytical study of the rich interplay between SPT physics and quantum criticality.

## Special QM Seminar Speaker Michal Papaj (MIT) Wednesday, November 11, 10:00 am

**Host** Ehud Altman**Time/Venue** Wednesday, November 11, 10:00 am Pacific Time via this link at Zoom.**Talk Title**: Segmented Fermi surfaces: discovery and applications**Abstract:** Since the early days of Bardeen-Cooper-Schrieffer theory, it has been predicted that a sufficiently large supercurrent can close the energy gap in a superconductor and creates gapless Bogoliubov quasiparticles through the Doppler shift of quasiparticle energy due to the Cooper pair momentum. In such gapless superconducting state, zero-energy quasiparticles reside on a segment of the normal state Fermi surface, while its remaining part is still gapped. In this talk I will discuss the recent discovery of such segmented Fermi surface in Bi2Te3 thin films proximitized by the superconductor NbSe2. The observation is based on quasiparticle interference technique and supported by extensive numerical modelling. I will then describe how the segmented Fermi surface can be used to induce a topological phase transition and create Majorana zero modes in quantum confined regions. Our results reveal the strong impact of finite Cooper pair momentum on the quasiparticle spectrum, and thus pave the way for further studies of states such as pair density wave and FFLO in unconventional superconductors.