Calendar
- 01November 1, 2022
CMSA Quantum Matter in Mathematics and Physics Seminar: Kardar-Parisi-Zhang dynamics in integrable quantum magnets
Although the equations of motion that govern quantum mechanics are well-known, understanding the emergent macroscopic behavior that arises from a particular set of microscopic interactions remains remarkably challenging. One particularly important behavior is that of hydrodynamical transport; when a quantum system has a conserved quantity (i.e. total spin), the late-time, coarse-grained dynamics of the conserved charge is expected to follow a simple, classical hydrodynamical description. However the nature and properties of this hydrodynamical description can depend on many details of the underlying interactions. For example, the presence of additional dynamical constraints can fundamentally alter the propagation of the conserved quantity and induce slower-than-diffusion propagation. At the same time, the presence of an extensive number of conserved quantities in the form of integrability, can imbue the system with stable quasi-particles that propagate ballistically through the system.In this talk, I will discuss another possibility that arises from the interplay of integrability and symmetry; in integrable one dimensional quantum magnets with complex symmetries, spin transport is neither ballistic nor diffusive, but rather superdiffusive. Using a novel method for the simulation of quantum dynamics (termed Density Matrix Truncation), I will present a detailed analysis of spin transport in a variety of integrable quantum magnets with various symmetries. Crucially, our analysis is not restricted to capturing the dynamical exponent of the transport dynamics and enables us to fully characterize its universality class: for all superdiffusive models, we find that transport falls under the celebrated Kardar-Parisi-Zhang (KPZ) universality class.
Finally, I will discuss how modern atomic, molecular and optical platforms provide an important bridge to connect the microscopic interactions to the resulting hydrodynamical transport dynamics. To this end, I will present recent experimental results, where this KPZ universal behavior was observed using atoms confined to an optical lattice.
[1] Universal Kardar-Parisi-Zhang dynamics in integrable quantum systems
B Ye†, FM*, J Kemp*, RB Hutson, NY Yao
(PRL in press) – arXiv:2205.02853[2] Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion
D Wei, A Rubio-Abadal, B Ye, FM, J Kemp, K Srakaew, S Hollerith, J Rui, S Gopalakrishnan, NY Yao, I Bloch, J Zeiher
Science (2022) — arXiv:2107.00038For information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/quantum-matter-seminar/
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https://forms.gle/1ewa7KeP6BxBuBeRA - 02November 2, 2022
CMSA Colloquium: Doping and inverting Mott insulators on semiconductor moire superlattices
CMSA, 20 Garden St, G1020 Garden Street, Cambridge, MA 02138Semiconductor bilayer heterostructures provide a remarkable platform for simulating Hubbard models on an emergent lattice defined by moire potential minima. As a hallmark of Hubbard model physics, the Mott insulator state with local magnetic moments has been observed at half filling of moire band. In this talk, I will describe new phases of matter that grow out of the canonical 120-degree antiferromagnetic Mott insulator on the triangular lattice. First, in an intermediate range of magnetic fields, doping this Mott insulator gives rise to a dilute gas of spin polarons, which form a pseudogap metal. Second, the application of an electric field between the two layers can invert the many-body gap of a charge-transfer Mott insulator, resulting in a continuous phase transition to a quantum anomalous Hall insulator with a chiral spin structure. Experimental results will be discussed and compared with theoretical predictions.
- 02November 2, 2022
Endoscopy for symmetric varieties
Science Center 5071 Oxford Street, Cambridge, MA 02138 USARelative trace formulas are central tools in the study of relative functoriality. In many cases of interest, basic stability problems have not previously been addressed. In this talk, I discuss a theory of endoscopy in the context of symmetric varieties with the global goal of stabilizing the associated relative trace formula. I outline how, using the dual group of the symmetric variety, one can give a good notion of endoscopic symmetric variety and conjecture a matching of relative orbital integrals in order to stabilize the relative trace formula, which can be proved in some cases. Time permitting, I will explain my proof of these conjectures in the case of unitary Friedberg–Jacquet periods.
- 02November 2, 2022
Informal Seminar: A norm for the homology of 3-manifolds
This seminar will be held in Science Center 530 at 4:00pm on Wednesday, November 2nd.
Please see the seminar page for more details: https://www.math.harvard.edu/~ctm/sem
- 02November 2, 2022
Harvard-MIT Combinatorics: $K$-rings of wonderful varieties and matroids
The wonderful variety of a realizable matroid and its Chow ring have played key roles in solving many long-standing open questions in combinatorics and algebraic geometry. Yet, its $K$-rings are underexplored until recently. I will be sharing with you some discoveries on the $K$-rings of the wonderful variety associated with a realizable matroid: an exceptional isomorphism between the $K$-ring and the Chow ring, with integral coefficients, and a Hirzebruch–Riemann–Roch-type formula. These generalize a recent construction of Berget–Eur–Spink–Tseng on the permutohedral variety. We also compute the Euler characteristic of every line bundle on wonderful varieties, and give a purely combinatorial formula. This in turn gives a new valuative invariant of an arbitrary matroid. As an application, we present the $K$-rings and compute the Euler characteristic of arbitrary line bundles of the Deligne–Mumford–Knudsen moduli spaces of rational stable curves with distinct marked points. Joint with Matt Larson, Sam Payne and Nick Proudfoot.
For more information on the speaker, please see: http://www.shiyue.li