Quantum Many-Body Physics in the Age of Quantum Information

Spontaneous symmetry breaking underpins some of the most important phenomena in condensed matter and statistical physics. A description of direct transitions between symmetry breaking phases in terms of local order parameters is formulated when the symmetry breaking patterns were Landau-compatible i.e. when the unbroken symmetries of one phase is a subset of the other. About twenty years ago, Senthil et al [1] demonstrated that a direct transition between Landau-incompatible symmetry breaking phases was also possible in two-dimensional quantum magnets. Such 'deconfined quantum critical' (DQC) transitions are believed to be exotic and found in interacting quantum systems, often with anomalous symmetries (e.g.: constrained by Lieb-Schultz-Mattis theorems).

In this talk, based on recent work with N. Jones [2], I will demonstrate that such special conditions are unnecessary and Landau-incompatible transitions can be found in a well-known family of classical statistical mechanical models introduced by Jose, Kadanoff, Kirkpatrick and Nelson [3]. All smoking-gun DQC features such as charged defect melting and enhanced symmetries are present and readily understood. I will also show that a closely related family of models also exhibits another unusual critical phenomenon found in quantum systems- 'unnecessary criticality' where a stable critical surface exists within a single phase of matter analogous to the first-order line separating liquid and gases.

[1] SCIENCE, Vol 303, Issue 5663
[2] arXiv: 2404.19009
[3] Phys. Rev. B 16, 1217 (1977)
 

One of the first nontrivial examples of quantum matter to be understood at equilibrium was the behavior of a chain of two-state spins, or qubits, entangled by nearest-neighbor interactions. Hans Bethe’s solution of the ground state in 1931 eventually led to the concept of Yang-Baxter integrability, and the thermodynamics were fully understood in the 1970s. However, the dynamical properties of this spin chain at any nonzero temperature remained perplexing until some unexpected theoretical and experimental progress beginning around 2019. Atomic emulators and quantum computers are beginning to complement solid-state quantum magnetism experiments, and computer scientists, physicists, and mathematicians all have their own reasons to care about the dynamics of simple arrangements of quantum spins. The last part of the talk covers how dynamics of more complicated spin models in higher dimensions are being used to search for emergent gauge fields and other phenomena.

Compositions are fundamental to how we understand the world, but in the quantum realm, they reveal a deeper and more profound complexity. In composite quantum systems, intriguing phenomena such as Bell nonlocality, quantum entanglement, and quantum discord emerge—features entirely absent in classical systems. These nonclassical correlations are crucial for developing advanced information and communication protocols. In this talk, drawing from our recent works, I will explore foundational aspects of composition as they apply to quantum systems. I will also discuss new insights into the nonclassical correlations arising in these systems, and introduce a novel form of composition in the temporal domain, proposing it as a new primitive for information processing.
 

Quantum resources have entered the many body stage over the last two decades. It is by now widely appreciated that entanglement plays a key role in characterizing physical phenomena, as diverse as topological order and critical behaviour. However, entanglement alone is not informative about state complexity, and in fact, it is only one side of the medal. In this talk, I will flip the coin and tackle quantum state complexity of many-body systems under the lense of non-stabilizerness - also known as magic. Magic quantifies the difficulty of realizing states in most error corrected codes, and is thus of fundamental practical importance. However, very little is known about its significance to many-body phenomena.

I will present method(s) to measure magic in tensor network simulations, and illustrate a series of applications to many body systems, including: (a) how state magic and long-range magic behave in conformal field theories - illustrating the limit of the former, and the capabilities of the latter; (b) how magic characterizes phases of lattice gauge theories, both in the context of spin liquids/error correction (toric code), and in the context of theories describing coupling between matter and light (Schwinger model); and (c) how our computational tools are presently more advanced than the largest scale experimental demonstration of magic in Rydberg atom quantum simulators.

Finally, I will discuss the broader impact of these findings on state complexity - indicating that realizing generic state quantum dynamics may require a very large amount of resources in error correcting quantum computers, but at the same time, providing interesting perspectives on new classes of variational states more powerful than tensor networks.
 

Computing methods on classical computers have dominated the discovery frontline from fundamental physics for several decades now. It is however becoming clear that at least in physics, there are several computational avenues (such as finite density and real-time dynamics) where development can be accelerated via quantum computers. At the same time, improving classical computing techniques using clever analytical insights is essential to provide further inputs to the quantum computing frontier. In this talk, we will discuss the broad ideas behind the novel constructions and selected applications illustrating results for realistic systems in condensed matter and particle physics. Such scenarios are expected to be realized in quantum hardware in the recent future.
 

Certain natural geometric properties of electron wavefunctions in a crystal turn out to explain a vast range of experimentally relevant properties. The original example was the explanation of the integer quantum Hall effect by Thouless and co-workers in terms of the “Berry curvature” derived from Bloch states. We now understand that a kind of gauge field in the Brillouin zone is the key to many equilibrium and linear-response properties, and current work is seeking to generalize these results to nonlinear and non-equilibrium properties as well. This talk reviews the basic concepts of wavefunction geometry starting from basic notions of undergraduate quantum mechanics, then covers more recent applications to new topological states, with a particular focus on effects beyond the standard adiabatic limit.

Quantum error correction (QEC) plays a critical role in preventing information loss in quantum systems and provides a framework for reliable quantum computation. However, implementing protocols for QEC and fault tolerance remains a challenge in the current era of noisy, intermediate-scale quantum (NISQ) processors. Here, we discuss recent progress in identifying resource-efficient strategies for QEC, which are tailored for the dominant noise processes affecting the quantum hardware. We show that such noise-adapted protocols can also provide a route to fault tolerance in near-term quantum devices, under certain assumptions.
 

Atomic and solid-state spin ensembles are promising platforms for implementing quantum technologies, but the unavoidable presence of noise imposes the needs for error correction. Typical quantum error correction (QEC) requires addressing specific qubits, but this is practically challenging in most realistic architectures. In this work, we propose QEC schemes for unresolvable spin ensembles. By using degenerate superpositions of excited states, which are fundamentally mixed, we find codes that can protect against both individual and collective errors, including dephasing, decay, and pumping. We show how information recovery can be achieved with only collective measurement and control, and illustrate its applications in extending memory lifetime. 

Ref: arXiv:2408.11628v1
 

Over the past two decades our understanding of the charge and heat transport properties of graphene has evolved progressively as the quality of the graphene devices improved. A key crossover occurs when the scattering between electrons themselves become more frequent than the scattering between electrons and disorder. In this regime, the electrons gas behaves as a hydrodynamic fluid, whose properties exhibit emergent universalities close to the charge neutrality point. In this talk, I shall present some new experimental result on the electrical and thermal transport measurements in very high-quality graphene devices where electron-electron scattering dominates over the momentum relaxation rate. I shall show that the transport in such graphene devices is unique in multiple ways, ranging from unconventional functional dependence of the dc conductivity on carrier density to giant violation of the Wiedemann-Franz law, where effective Lorenz number varies over six orders of magnitude with carrier density. We find that the transport properties of ultra-clean graphene close to charge neutrality are quantitatively consistent with that of a hydrodynamic Dirac fluid where both charge and heart flow are determined by a single universal transport constant.
 

Common intuition tells us that if one part of an interacting system is continuously cooled, the other parts should also cool down. This intuition can be put on firm grounds for the case of Markovian cooling of a free-fermion "lead" that is locally coupled to a generic quantum system. I will talk about a scenario where the opposite happens, namely, the system heats up toward its most excited state as the lead is cooled (or vice versa), even if other parameters favor sympathetic cooling. This dramatic effect originates from a simple but structured coupling that preserves a U(1) charge, and is realizable as existing setups.

Quantum steering is a protocol made up of successive measurements of the system, employing the back-action generated to push the system towards a desired target state. The latter may be the ground state of the system’s Hamiltonian, thus cooling the system to “zero temperature”. I will address here two questions: (1) Can we achieve such cooling by acting only on a small section of the system (a protocol we denote “dilute cooling”)? (2) When such cooling to zero
temperature is not feasible - how low in temperature can we go?
 

The string-net model introduced by M. Levin and X.-G. Wen in 2005 allows one to generate all (bosonic) topological  achiral phases in two dimensions. In this talk, I will explain how to compute the exact partition function of this model and discuss the finite-temperature properties of several quantities such as the topological mutual information. These results show that, in this context, topological order can only survive up to a temperature which depends on the system size and goes to zero in the thermodynamical limit.