Condensed Matter

It is an open question how well tensor network states in the form of an infinite projected entangled-pair states (iPEPS) tensor network can approximate gapless quantum states of matter. In this talk we address this issue for two different physical scenarios: (i) a conformally invariant (2+1)d quantum critical point in the incarnation of the transverse-field Ising model on the square lattice and (ii) spontaneously broken continuous symmetries with gapless Goldstone modes exemplified by the S=1/2 antiferromagnetic Heisenberg and XY models on the square lattice. We find that the energetically best wave functions display finite correlation lengths and we introduce a powerful finite correlation length scaling framework for the analysis of such finite bond dimension (finite-D) iPEPS states. The framework is important (i) to understand the mild limitations of the finite-D iPEPS manifold in representing Lorentz-invariant, gapless many-body quantum states and (ii) to put forward a practical scheme in which the finite correlation length ξ(D) combined with field theory inspired formulas can be used to extrapolate the data to infinite correlation length, i.e., to the thermodynamic limit. The finite correlation length scaling framework opens the way for further exploration of quantum matter with an (expected) Lorentz-invariant, massless low-energy description, with many applications ranging from condensed matter to high-energy physics.

In the first half, I will demonstrate an efficient and general approach for realizing non-trivial quantum states, such as quantum critical and topologically ordered states, in quantum simulators. In the second half, I will present a related variational ansatz for many-body quantum systems that is remarkably efficient. In particular, representing the critical point of the one-dimensional transverse field Ising model only requires a number of variational parameters scaling logarithmically with system size. Though optimizing the ansatz generally requires Monte Carlo sampling, our ansatz potentially enables a partial mitigation of the sign problem at the expense of having to optimize a few parameters.

We introduce an isometric restriction of the tensor-network ansatz that allows for highly efficient contraction of the network. We consider two concrete applications using this ansatz. First, we show that a matrix-product state representation of a 2D quantum state can be iteratively transformed into an isometric 2D tensor network. Second, we introduce a 2D version of the time-evolving block decimation algorithm (TEBD2) for approximating the ground state of a Hamiltonian as an isometric tensor network, which we demonstrate for the 2D transverse field Ising model.

In the context of quantum spin liquids, it is long known that the condensation of fractionalized excitations will inevitably break certain physical symmetries sometimes. For example, condensing spinons will usually break spin rotation and time reversal symmetries. We generalize these phenomena to generic continuous quantum phase transitions between symmetry enriched topological orders driven by anyon condensation. We provide a generic rule to determine whether a symmetry is enforced to break across an anyon condensation transition. Using a dimensional reduction scheme, we establish a mapping between these symmetry-breaking anyon-condensation transitions in two spatial dimensions, and deconfined quantum criticality in one spatial dimension.

The Hallmark of strongly entangled quantum phases is an intrinsic impossibility to describe them locally in terms of microscopic degrees of freedom. Two popular methods that have been developed to analytically describe these exotic states are known as (1) ‘parton construction’ and (2) ‘coupled-wire approach’. The former provides a constructive route for determining which non-trivial phases may arise, in principle, for a given set of constituent degrees of freedom and symmetries. This capability comes at the expense of having very little predictive power what phases do arise, in practice, in any particular system. The latter technique, by contrast, yields explicit expressions of ground states, excitations as well as parent Hamiltonians in terms of microscopic degrees of freedom. The price to pay is a lack of flexibility, and each phase needs to be analyzed on a laborious case-by-case basis. I will show how recent understanding of two-dimensional dualities provides a natural link between the two approaches. Specifically, I will show how a wide range of parton mean-field states can be easily translated into explicit coupled-wire models, and how their universal properties can be obtained in a transparent manner.

We perform both numerical and theoretical studies on the phase diagram of the Kitaev materials in the presence of a magnetic field. We find that a new quantum spin liquid state with neutral Fermi surfaces emerges at intermediate field strengths, between the regimes for the non-Abelian chiral spin liquid state and for the trivial polarized state. We discuss the exotic field-induced quantum phase transitions from this new state with neutral Fermi surfaces to its nearby phases. We also theoretically study the field-induced quantum phase transitions from the non-Abelian chiral spin liquid to the symmetry-broken zigzag phase and to the trivial polarized state. Utilizing the recently developed dualities of gauge theories, we find these transitions can be described by critical bosons or gapless fermions coupled to emergent non-Abelian gauge fields, and the critical theories are of the type of a QCD3-Chern-Simons theory. We propose that all these exotic quantum phase transitions can potentially be direct and continuous in the Kitaev materials, and we present sound evidence for this proposal. Therefore, besides being systems with intriguing quantum magnetism, Kitaev materials may also serve as table-top experimental platforms to study the interesting dynamics of emergent strongly interacting quarks and gluons in 2+1 dimensions. Finally, we address the experimental signatures of these phenomena.

I will describe an infinite set of exotic gauge theories that have recently and simultaneously emerged in several a priori unrelated areas of condensed matter physics such as self-correcting quantum memory, topological order in 3+1 dimensions, spin liquids and quantum elasticity. In these theories the gauge field is a symmetric tensor (not to be confused with higher form, which is an anti-symmetric tensor), or in more exotic situations, the gauge fields do not have a well-defined transformation properties under rotations. I will discuss a few exotic features of these theories such as (i) corresponding Gauss law constraints (ii) failure of the gauge invariance in curved space, (iii) the nature of the gauge group, etc. I will also discuss the what kind of matter such theories can couple to. It turns out that the corresponding matter must conserve electric charge and various multipole moments of the electric charge (or number) density. The conservation laws of multipole moments lead to dramatic consequences for the dynamics. I will also discuss how such theories can be obtained by gauging a global symmetry. Finally, I will discuss non-local operators in this type of theories. Remarkably, in addition to more-or-less expected Wilson line and surface operators, such theories exhibit (at least upon discretization on a lattice) non-local operators supported on a space of fractional dimension (in between line and surfaces).

Two topics have been gaining momentum in different fields of physics: At the intersection of condensed matter and high-energy physics lies the out-of-time-ordered correlator (OTOC). The OTOC reflects quantum many-body equilibration; chaos; and scrambling, the spread of quantum information through many-body entanglement. In quantum optics and quantum foundations, quasiprobabilities resemble probabilities but can become negative and nonreal. Such nonclassical values can signal nonclassical physics, such as the capacity for superclassical computation. I unite these two topics, showing that the OTOC equals an average over a quasiprobability distribution. The distribution, a set of numbers, contains more information than the OTOC, one number that follows from coarse-graining over the distribution. Aside from providing insight into the OTOC’s fundamental nature, the OTOC quasiprobability has several applications: Theoretically, the quasiprobability interrelates scrambling with uncertainty relations, nonequilibrium statistical mechanics, and chaos. Experimentally, the quasiprobability points to a scheme for measuring the OTOC (via weak measurements, which refrain from disturbing the measured system much). The quasiprobability also signals false positives in attempts to measure scrambling of open systems. Finally, the quasiprobability underlies a quantum advantage in metrology. References • NYH, Phys. Rev. A 95, 012120 (2017). https://journals.aps.org/pra/abstract/10.1103/PhysRevA.95.012120 • NYH, Swingle, and Dressel, Phys. Rev. A 97, 042105 (2018). https://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.042105 • NYH, Bartolotta, and Pollack, accepted by Comms. Phys. (in press). https://arxiv.org/abs/1806.04147 • Gonzàlez Alonso, NYH, and Dressel, Phys. Rev. Lett. 122, 040404 (2019). https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.122.040404 • Swingle and NYH, Phys. Rev. A 97, 062113 (2018). https://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.062113 • Dressel, Gonzàlez Alonso, Waegell, and NYH, Phys. Rev. A 98, 012132 (2018). https://journals.aps.org/pra/abstract/10.1103/PhysRevA.98.012132 • Arvidsson-Shukur, NYH, Lepage, Lasek, Barnes, and Lloyd, arXiv:1903.02563 (2019). https://arxiv.org/abs/1903.02563

The fine grained energy spectrum of quantum chaotic systems, which are widely believed to be characterized by random matrix statistics. A basic scale in these systems is the energy range over which this behavior persists. We defined the corresponding time scale by the time at which the linearly growing ramp region in the spectral form factor begins. We dubbed this ramp time. It is also referred to as the ergodic or Thouless time in the condensed matter physics community. The purpose of my talk is to understand this scale in many-body quantum systems that display strong chaos (such as SYK and spin chain), sometimes referred to as scrambling systems. Using numerical results and analytic estimates for random quantum circuits, I will provide summary of results on scaling of ramp time with system size in the presence/absence of conservation laws.