Quantum Matter

The presence of many competing classical ground states in frustrated magnets implies that quantum fluctuations may stabilize quantum spin liquids (QSL), which are characterized by fractionalized excitations and emergent gauge fields. A paradigmatic example is the U(1) Dirac spin liquid (DSL), which at low-energies is described by emergent quantum electrodynamics in 2+1 dimensions (QED3), a strongly interacting field theory with conformal symmetry. While the DSL is believed to be intrinsically stable, its robustness against various other couplings has been largely unexplored and is a timely question, also given recent experiments on triangular-lattice rare-earth oxides. In this talk, using complementary perturbation theory and scaling arguments as well as results from numerical DMRG simulations, I will show that a symmetry-allowed coupling between (classical) finite-wavevector lattice distortions and monopole operators of the U(1) Dirac spin liquid generally induces a spin-Peierls instability towards a (confining) valence-bond solid state. Away from the limit of static distortions, I will argue that the phonon energy gap establishes a parameter regime where the spin liquid is expected to be stable.

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Zoom link https://pitp.zoom.us/j/96764903405?pwd=Y0gyU3hGSC9va0hzWnZRZFBOVmRCZz09

Quantum Hall phases are the most exotic experimentally established quantum phases of matter.Recently they have been discovered at zero external magnetic field in two dimensional moire materials. I will describe recent work (with Xue-Yang Song and Ya-Hui Zhang) on their proximate phases and associated phase transitions that is motivated by the high tunability of thede moire systems. These phase transitions (and some of the proximate phases) are exotic as well, and realize novel ‘beyond Landau’ criticality that have been explored theoretically for many years. I will show that these moiré platforms provide a great experimental opportunity to study these unconventional phase transitions and related unconventional phases, thereby opening a new direction for research in quantum matter.

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Zoom link : https://pitp.zoom.us/j/97483204701?pwd=S2x4ck9tNHFjM0RiTDNWNFhaMk9SUT09

An ongoing program of work in statistical physics and quantum dynamics is concerned with understanding the character of systems which follow an unconventional approach towards thermal equilibrium. In this talk, I will add to this story by introducing examples of simple 1D systems---both classical and quantum---which thermalize in very unusual ways. These examples have dynamics which is strictly local and translation-invariant, but in spite of this, they: a) can have very long thermalization times, with expectation values of local operators relaxing only over times exponential in the system size; and b) can thermalize only when they are placed in extremely large baths, with the required bath size growing exponentially (or even faster) in system size. Proofs of these results will be given using techniques from geometric group theory, a beautiful area of mathematics concerned with the complexity and geometry of infinite discrete groups. This talk will be based on a paper in preparation with Shankar Balasubramanian, Sarang Golaparakrishnan, and Alexey Khudorozhkov.

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Zoom link: https://pitp.zoom.us/j/99430001465?pwd=NENlS1M5UGc5UWM1ekQvRWFrZGYyUT09

We study the Petz map, which is a universal recovery channel of a tripartite quantum state upon erasing one party, in quantum many-body systems. The fidelity of the recovered state with the original state quantifies how much information shared by the two parties is not mediated by one of the party, and has a universal lower bound in terms of the conditional mutual information (CMI). I will study this quantity in two different contexts. First, in a CFT ground state, we show that the fidelity is universal, which means it only depends on the central charge and the cross ratio. We compute this universal function numerically and show that it is consistently better than the naive CMI bound. Secondly, we show that for two broad classes of the states, the CMI lower bound is saturated. These include stabilizer states (in any dimensions) and the ground state of 2+1D topological order.

Zoom link: https://pitp.zoom.us/j/92623435839?pwd=N1JIdkUwWHFkZGpqb1p1V3NKYy91QT09

The notorious exponential complexity of quantum problems can be avoided for systems with limited correlations. For example, states of one-dimensional systems with bounded entanglement are approximable by matrix product states. We consider fermionic systems, where correlations can be defined as deviations from Gaussian states. Heuristically, one expects a link between compact non-Gaussian ansatzes and bounded fermionic correlations. This connection, however, has not been rigorously demonstrated. Our work resolves this conceptual gap.

We focus on pure states with a fixed number of fermions. Generalizing the so-called Plücker relations, we introduce k-particle correlation measures ω_k. The vanishing of ω_k at a constant k defines a class H_k of states with limited correlations. These sets H_k are nested, ranging from Gaussian for k=1 to the full n-fermion Hilbert space H for k=n+1. States in H_{k=O(1)} can be represented using a non-Gaussian ansatz of polynomial size. Classes H_k have physical meaning, containing all truncated perturbation series around Gaussian states. We also identify non-perturbative examples of states in H_{k=O(1)}, by a numerical study of excited states in the 1D Hubbard model. Finally, we discuss the information-theoretic implications of our results for the widely used coupled-cluster ansatz.

Zoom Link: TBD

Neural quantum states (NQSs) have emerged as a novel promising numerical method to solve the quantum many-body problem. However, it has remained a central challenge to train modern large-scale deep network architectures to desired quantum state accuracy, which would be vital in utilizing the full power of NQSs and making them competitive or superior to conventional numerical approaches. Here, we propose a minimum-step stochastic reconfiguration (MinSR) method that reduces the optimization complexity by orders of magnitude while keeping similar accuracy as compared to conventional stochastic reconfiguration. MinSR allows for accurate training on unprecedentedly deep NQS with up to 64 layers and more than 105 parameters in the spin-1/2 Heisenberg J1-J2 models on the square lattice. We find that this approach yields better variational energies as compared to existing numerical results and we further observe that the accuracy of our ground state calculations approaches different levels of machine precision on modern GPU and TPU hardware. The MinSR method opens up the potential to make NQS superior as compared to conventional computational methods with the capability to address yet inaccessible regimes for two-dimensional quantum matter in the future.

How do you control something you can not look at? For controlling quantum systems, information on the system’s state could come through weak measurements. Such measurements provide some information, but will inevitably also perturb the system, meaning there is noise both in the state estimation as well as in the measurement. We study a simple single particle quantum setup (the quantum equivalent of the instability problem known as the cartpole problem) and investigate several control methods including reinforcement learning, and compare their performance.

Our universe is quantum, but our everyday experience is classical. Where is the boundary between quantum and classical worlds? How does classical reality emerge in quantum many-body systems? Does the collapse of the quantum states involve intelligence? These are fundamental questions that have puzzled physicists and philosophers for centuries. The recent development of quantum information science and artificial intelligence offers new opportunities to investigate these old problems. In this talk, we present our preliminary research on using a transformer-based language model to process randomized measurement data collected from Schrödinger’s cat quantum state. We show that the classical reality emerges in the language model due to the information bottleneck: although our training data contains the full quantum information of Schrödinger’s cat, a weak language model can only learn the classical reality of the cat from the data. Our study opens up a new avenue for using the big data generated on noisy intermediate-scale quantum (NISQ) devices to train generative models for representation learning of quantum operators, which might be a step toward our ultimate goal of creating an artificial intelligence quantum physicist.