Benedikt Placke

Abstract:

We study the non-unitary dynamics of a class of quantum circuits based on stochastically measuring check operators of subsystem quantum error-correcting codes, such as the Bacon-Shor code and its various generalizations. Our focus is on how properties of the underlying code are imprinted onto the measurement-only dynamics. We find that in a large class of codes with nonlocal stabilizer generators, at late times there is generically a nonlocal contribution to the subsystem entanglement entropy which scales with the subsystem size. The nonlocal stabilizer generators can also induce slow dynamics, since depending on the rate of competing measurements the associated degrees of freedom can take exponentially long (in system size) to purify (disentangle from the environment when starting from a mixed state) and to scramble (become entangled with the rest of the system when starting from a product state). Concretely, we consider circuits for which the nonlocal stabilizer generators of the underlying subsystem code take the form of subsystem symmetries. We present a systematic study of the phase diagrams and relevant time scales in two and three spatial dimensions for both Calderbank-Shor-Steane (CSS) and non-CSS codes, focusing in particular on the link between slow measurement-only dynamics and the geometry of the subsystem symmetry. A key finding of our work is that slowly purifying or scrambling degrees of freedom appear to emerge only in codes whose subsystem symmetries are nonlocally generated, a strict subset of those whose symmetries are simply nonlocal. We comment on the link between our results on subsystem codes and the phenomenon of Hilbert-space fragmentation in light of their shared algebraic structure.

Abstract:

The insulating magnetic pyrochlore ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ has gained attention as a quantum spin-ice candidate with dipole-octupole character that arises from the crystal-electric-field ground-state doublet for the ${\mathrm{Ce}}^{3+}$ Kramers ion. This dipole-octupole character permits both spin-ice phases based on magnetic dipoles and those based on more-exotic octupoles. This work reports low-temperature neutron diffraction measurements on single-crystal ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ with $Q$ coverage both at low $Q$ , where the magnetic form factor for dipoles is near maximal, and at high $Q$ , covering the region where the magnetic form factor for ${\mathrm{Ce}}^{3+}$ octupoles is near maximal. This study was motivated by recent powder neutron diffraction studies of other Ce-based dipole-octupole pyrochlores, ${\mathrm{Ce}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$ and ${\mathrm{Ce}}_2{\mathrm{Hf}}_2{\mathrm{O}}_7$ , which each showed temperature-dependent diffuse diffraction at high $Q$ , interpreted as arising from octupolar correlations. Our measurements use an optimized single-crystal diffuse scattering instrument that allows us to screen against strong Bragg scattering from ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ . The temperature-difference neutron diffraction reveals a low- $Q$ peak consistent with dipolar spin-ice correlations reported in previous work, and an alternation between positive and negative net intensity at higher $Q$ . These features are consistent with our numerical-linked-cluster calculations using pseudospin interaction parameters previously reported for ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ , ${\mathrm{Ce}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$ , and ${\mathrm{Ce}}_2{\mathrm{Hf}}_2{\mathrm{O}}_7$ . Importantly, neither the measured data nor any of the NLC calculations show evidence for increased scattering at high $Q$ resulting from octupolar correlations. We conclude that at the lowest attainable temperature for our measurements ( $T=0.05\mathrm{K}$ ), scattering from octupolar correlations in ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ is not present in the neutron diffraction signal on the level of our observation threshold of around 0.1% of the low- $Q$ dipole scattering. We compare these results to those obtained earlier on powder ${\mathrm{Ce}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$ and ${\mathrm{Ce}}_2{\mathrm{Hf}}_2{\mathrm{O}}_7$ , and to low-energy inelastic neutron scattering from single-crystal ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ .

Abstract:

We study a classical Ising model on the honeycomb lattice with local two-body interactions and present strong evidence that at low temperature it realizes a higher-rank Coulomb liquid with fracton excitations. We show that the excitations are (type-I) fractons, appearing at the corners of membranes of spin flips. Because of the threefold rotational symmetry of the honeycomb lattice, these membranes can be locally combined such that no excitations are created, giving rise to a set of ground states described as a liquid of membranes. We devise a cluster Monte Carlo algorithm purposefully designed for this problem that moves pairs of defects, and use it to study the finite-temperature behavior of the model. We show evidence for a first order transition from a high-temperature paramagnet to a low-temperature phase whose correlations precisely match those predicted for a higher-rank Coulomb phase.

Abstract:

The dipolar-octupolar (DO) pyrochlores, R2M2O7 (R=Ce,Sm,Nd), are key players in the search for realizable novel quantum spin liquid (QSL) states as a large parameter space within the DO pyrochlore phase diagram is theorized to host QSL states of both dipolar and octupolar nature. New single crystals and powders of Ce2Sn2O7, synthesized by hydrothermal techniques, present an opportunity for a new characterization of the exchange parameters in Ce2Sn2O7 using the near-neighbor XYZ model Hamiltonian associated with DO pyrochlores. Utilizing quantum numerical linked cluster expansion fits to heat capacity and magnetic susceptibility measurements, and classical Monte Carlo calculations to the diffuse neutron diffraction of the new hydrothermally grown Ce2Sn2O7 samples, we place Ce2Sn2O7's ground state within the ordered dipolar all-in-all-out (AIAO) Néel phase, with quantum Monte Carlo calculations showing a transition to long-range order at temperatures below those accessed experimentally. Indeed, our new neutron diffraction measurements on the hydrothermally grown Ce2Sn2O7 powders show a broad signal at low scattering wave vectors, reminiscent of a dipolar spin ice, in striking contrast from previous powder neutron diffraction on samples grown from solid-state synthesis, which found diffuse scattering at high scattering wave vectors associated with magnetic octupoles and suggested an octupolar quantum spin ice state. We conclude that new hydrothermally grown Ce2Sn2O7 samples host a finite-temperature proximate dipolar spin ice phase, above the expected transition to AIAO Néel order.

Abstract:

We propose a simple family of valence-bond crystals as potential ground states of the S=1/2 and S=1 Heisenberg antiferromagnet on the pyrochlore lattice. Exponentially numerous in the linear size of the system, these can be visualized as hard-hexagon coverings, with each hexagon representing a resonating valence-bond ring. This ensemble spontaneously breaks rotation, inversion, and translation symmetries. A simple, yet accurate, variational wave function allows a precise determination of the energy, confirmed by the density matrix renormalization group and numerical linked cluster expansion, and extended by an analysis of excited states. The identification of the origin of the stability indicates applicability to a broad class of frustrated lattices, which we demonstrate for the checkerboard and ruby lattices. Our work suggests a perspective on such quantum magnets, in which unfrustrated motifs are effectively uncoupled by the frustration of their interactions.