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.

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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

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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.

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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.

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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.

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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.

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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.

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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.

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Special QM Seminar Speaker Sam Garratt (Oxford) Wednesday, October 21, 10:15 am

Host Ehud Altman
Time/Venue Wednesday, October 21, 10:15 am Pacific Time via Zoom
Talk Title: Many-body quantum chaos and the local pairing of Feynman histories
Abstract I will discuss many-body quantum dynamics under random Floquet circuits, simple examples of systems with local interactions that support ergodic phases. Quite generally, physical properties can be expressed in terms of multiple sums over Feynman histories, which for these models are paths or many-body orbits in Fock space. A natural simplification of such sums is the diagonal approximation, where the only terms that are retained are ones in which each path is paired with a partner that carries the complex conjugate weight. Our central result is to show how the diagonal approximation must be extended in many-body systems with local interactions. This leads to deviations of spectral statistics from random matrix theory, and of matrix element correlations from the eigenstate thermalisation hypothesis. Strikingly, both kinds of deviation diverge with system size. If there is time, I will also discuss the connection to the entanglement membrane, known to characterise the scrambling of quantum information.

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Special QM/AMO Joint Seminar Speakers Kaoru Mizuta & Yoshihiro Michishita (Kyoto University) Monday, March 9, 4:15 pm in 325 LeConte

Host Joel Moore
Time/Venue Monday, March 9, 4:15 – 5:15 pm in 325 LeConte
Kaoru Mizuta Talk Title Floquet engineering with emergent symmetries: Control of symmetry protected topological phases
Kaoru Mizuta Abstract
Recently periodically driven (Floquet) systems have attracted much interested, and Floquet engineering, control of phases by a periodic drive, is one of the most vigorous fields in Floquet systems. However, in conventional Floquet engineering, only high-frequency drives (=drives whose energy scale is much smaller than the frequency) are mainly utilized since it is based on high-frequency expansion theory, only applicable to Floquet systems under high-frequency drives.
Therefore, we extend the conventional high-frequency expansion theory to the cases in the presence of resonant drives (= drives whose local energy scale is comparable to the frequency) and propose a new scheme of Floquet engineering done by high-frequency and resonant drives [1]. We clarify that the effective Hamiltonian describing long-time dynamics acquires an emergent Z_N symmetry, and hence our scheme enables us to simultaneously control phases and add a symmetry to the system. With our Floquet engineering, we also propose a way to realize/control topological phases protected by a Z_2×Z_2 symmetry only in the presence of a Z_2 symmetry [2].
[References]
[1] K. Mizuta, K. Takasan, and Norio Kawakami, Phys. Rev. B 100, 020301(R) (2019)
[2] K. Mizuta, K. Takasan, and Norio Kawakami, Phys. Rev. A 100, 0521009 (2019)
Yoshihiro Michishita Talk Title Property as open quantum systems and the nonhermiticity in strongly-correlated electron systems
The phenomena described by the non-hermitian Hamiltonian has been intensively studied especially in the context of artificial quantum systems[1-4]. Effective non-hermitian Hamiltonian induces novel topological phases[1,2], unusual critical phenomena[3], enhanced sensitivity[4] , and so on.
Yoshihiro Michishita Abstract The phenomena described by the non-hermitian Hamiltonian has been intensively studied especially in the context of artificial quantum systems[1-4]. Effective non-hermitian Hamiltonian induces novel topological phases[1,2], unusual critical phenomena[3], enhanced sensitivity[4] , and so on.
In the open quantum systems(OQS), such as cold atomic systems, it is possible to deribe an effective non-hermitian Hamiltonian under certain conditions even though the Hamiltonian describing the total system is hermitian. However, as the system becomes larger, it becomes difficult to experimentally realize these conditions, such as postselection or a PT-symmetric setup. Thus, experiments about nonhermitian phenomena in artificial quantum systems are particularly done in one-dimensional or small systems.
On the other hand, in strongly-correlated electron systems(SCES), it is also possible to derive the effective non-hermitian Hamiltonian determining the spectral function[5]. In this case, the non-hermiticity comes from the scattering by interaction and the certain setup, such as post selection or PT-symmetric setup, is not necessary. Thus, it seems to be easier to observe the bulk 2D or 3D non-hermitian phenomena in SCES than in OQS. The non-hermitian physics in SCES also hold the potential to explain the pseudo-gap in curate superconductors or quantum oscillation[6] in the topological Kondo insulator SmB6 and YbB12. Therefore the non-hermitian physics in SCES is also studied intensively today[7].
One problem is that the way to introduce the effective non-hermitian Hamiltonian in each context is quite different and it is not clear their relation, especially whether they are the same or not.
We close this gap and demonstrate that the non-hermitian Hamiltonians emerging in both fields are identical, and we clarify the why postselection is not necessary to derive a non-hermitian Hamiltonian in strongly correlated materials[8]. Using this knowledge, we propose a method to analyze non-hermitian properties without the necessity of postselection by studying specific response functions of open quantum systems and strongly-correlated systems. We have also shown that non-markovness of the dynamics of the single particles in strongly-correlated electron systems is relevant.
In this seminar, I will shortly explain about the difference between the non-hermitian Hamiltonian in SCES and that in OQS and talk about our recent work[7,8]. I look forward to your participation.
References:
[1] H. Shen, B. Zhen, and L. Fu, Phys. Rev. Lett. 120, 146402 (2018)
[2] Z. Gong, Y. Ashida, K. Kawabata, K. Takasan, S. Higashikawa, and M. Ueda, Phys. Rev. X 8, 031079 (2018)
[3] Y. Ashida, S. Furukawa, and M. Ueda, Nature communications 8, 15791 (2017)
[4] W. Chen, S ̧. K. Özdemir, G. Zhao, J. Wiersig, and L. Yang, Nature 548, 192 (2017)
[5]V. Kozii and L. Fu, arXiv:1708.05841 (2017)
[6]H. Shen and L. Fu, Phys. Rev. Lett. 121, 026403 (2018)
[7]Y. Michishita, T. Yoshida and R. Peters PRB: 101(8),085122(2020)
[8]Y. Michishita, and R. Peters arXiv: 2001.09045(2020)

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