Stable Measurement-Induced Floquet Enriched Topological Order.

The Floquet code utilizes a periodic sequence of two-qubit measurements to realize the topological order. After each measurement round, the instantaneous stabilizer group can be mapped to a honeycomb toric code, explaining the topological feature. The code also possesses a time-crystal order-the e-m transmutation after every cycle, breaking the Floquet symmetry of the measurement schedule. This behavior is distinct from the stationary topological order realized in either random circuits or time-independent Hamiltonian. Therefore, the resultant phase belongs to the overlap between the classes of Floquet enriched topological orders and measurement-induced phases. In this Letter, we construct a continuous path interpolating between the Floquet and toric codes, focusing on the transition between the time-crystal and stationary topological phases. We show that this transition is characterized by a divergent length scale. We also add single-qubit perturbations to the model and obtain a richer two-dimensional parametric phase diagram of the Floquet code, showing the stability of the Floquet enriched topological order.

Lithium isotopes differentially modify mitochondrial amorphous calcium phosphate cluster size distribution and calcium capacity.

Lithium is commonly prescribed as a mood stabilizer in a variety of mental health conditions, yet its molecular mode of action is incompletely understood. Many cellular events associated with lithium appear tied to mitochondrial function. Further, recent evidence suggests that lithium bioactivities are isotope specific. Here we focus on lithium effects related to mitochondrial calcium handling. Lithium protected against calcium-induced permeability transition and decreased the calcium capacity of liver mitochondria at a clinically relevant concentration. In contrast, brain mitochondrial calcium capacity was increased by lithium. Surprisingly, 7Li acted more potently than 6Li on calcium capacity, yet 6Li was more effective at delaying permeability transition. The size distribution of amorphous calcium phosphate colloids formed in vitro was differentially affected by lithium isotopes, providing a mechanistic basis for the observed isotope specific effects on mitochondrial calcium handling. This work highlights a need to better understand how mitochondrial calcium stores are structurally regulated and provides key considerations for future formulations of lithium-based therapeutics.

Cross Entropy Benchmark for Measurement-Induced Phase Transitions.

We investigate prospects of employing the linear cross entropy to experimentally access measurement-induced phase transitions without requiring any postselection of quantum trajectories. For two random circuits that are identical in the bulk but with different initial states, the linear cross entropy χ between the bulk measurement outcome distributions in the two circuits acts as an order parameter, and can be used to distinguish the volume law from area law phases. In the volume law phase (and in the thermodynamic limit) the bulk measurements cannot distinguish between the two different initial states, and χ=1. In the area law phase χ<1. For circuits with Clifford gates, we provide numerical evidence that χ can be sampled to accuracy ϵ from O(1/ϵ^{2}) trajectories, by running the first circuit on a quantum simulator without postselection, aided by a classical simulation of the second. We also find that for weak depolarizing noise the signature of the measurement-induced phase transitions is still present for intermediate system sizes. In our protocol we have the freedom of choosing initial states such that the "classical" side can be simulated efficiently, while simulating the "quantum" side is still classically hard.

Phosphates form spectroscopically dark state assemblies in common aqueous solutions.

Phosphates and polyphosphates play ubiquitous roles in biology as integral structural components of cell membranes and bone, or as vehicles of energy storage via adenosine triphosphate and phosphocreatine. The solution phase space of phosphate species appears more complex than previously known. We present nuclear magnetic resonance (NMR) and cryogenic transmission electron microscopy (cryo-TEM) experiments that suggest phosphate species including orthophosphates, pyrophosphates, and adenosine phosphates associate into dynamic assemblies in dilute solutions that are spectroscopically "dark." Cryo-TEM provides visual evidence of the formation of spherical assemblies tens of nanometers in size, while NMR indicates that a majority population of phosphates remain as unassociated ions in exchange with spectroscopically invisible assemblies. The formation of these assemblies is reversibly and entropically driven by the partial dehydration of phosphate groups, as verified by diffusion-ordered spectroscopy (DOSY), indicating a thermodynamic state of assembly held together by multivalent interactions between the phosphates. Molecular dynamics simulations further corroborate that orthophosphates readily cluster in aqueous solutions. This study presents the surprising discovery that phosphate-containing molecules, ubiquitously present in the biological milieu, can readily form dynamic assemblies under a wide range of commonly used solution conditions, highlighting a hitherto unreported property of phosphate's native state in biological solutions.

Differential effects of lithium isotopes in a ketamine-induced hyperactivity model of mania.

Sub-anesthetic doses of ketamine produce an increase in rodent ambulation that is attenuated by co-administration of naturally-occurring lithium (LiN), the drug most commonly employed in the treatment of bipolar illness. As a consequence, ketamine-induced hyperactivity has been proposed as an animal model of manic behavior. The current study employed a modified version of this model to compare the potency of LiN to that of each of its two stable isotopes - lithium-6 (Li-6) and lithium-7 (Li-7). Since Li-7 constitutes 92.4% of the parent compound it was hypothesized to produce comparable behavioral effects to that of LiN. The current study was devised to determine whether Li-6 might be more, less, or equally effective at tempering hyperactivity relative to Li-7 or to LiN in an animal model of manic behavior. Male rats were maintained on a restricted but high-incentive diet containing a daily dose of 2.0 mEq/kg of lithium (LiN), Li-6 or Li-7 for 30 days. A control group consumed a diet infused with sodium chloride (NaCl) in place of lithium to control for the salty taste of the food. On day 30, baseline testing revealed no differences in the locomotor behavior among the four treatment groups. Animals then continued their Li/NaCl diets for an additional 11 days during which every subject received a single IP injection of either ketamine (25 mg/kg) or 0.9% physiological saline. On the final four days of this regimen, locomotor activity was assessed during 60 min sessions each beginning immediately after ketamine injection. While all three lithium groups produced comparable decreases in ketamine-induced hyperactivity on the first trial, by the fourth trial Li-6 animals exhibited significantly greater and more prolonged reductions in hyperactivity compared to either Li-7 and Li. These results suggest that Li-6 may be more effective at treating mania than its parent compound.

Effects of chronic lithium exposure in a modified rodent ketamine-induced hyperactivity model of mania.

Bipolar illness is characterized by periods of "mania" - high energy, irritability, and increased psychomotor activation. While the neurobiological investigation of mania has been limited by the lack of reliable animal models, researchers have recently reported that daily subanesthetic doses of ketamine produce a lithium-reversible increase in rodent locomotor activity. Such studies have typically employed short-term (2 week) exposure to daily intraperitoneal-injected lithium and extremely brief (i.e., 5-min) open-field tests of hyperactivity. To increase the translational utility of the model, the effects of 70-days of orally administered lithium were examined on ketamine-induced hyperlocomotion during 30-min test sessions. Rats consumed 2.0 mEq/kg lithium chloride (LiCl) presented daily in a high incentive food (10 g of peanut butter). Control animals ingested peanut butter infused with an equimolar concentration of sodium chloride (NaCl). After 60 days of treatment, a 30-min baseline revealed no differences in the locomotor activity of LiCl and NaCl animals. During the next 10 days, animals received single daily supplemental injections of 25 mg/kg IP ketamine. A subset of animals was injected daily with saline and served as non-ketamine controls. Behavioral testing on the final two days of treatment confirmed that ketamine administration produced a profound increase in locomotor activity that was significantly attenuated in the LiCl group. Additionally, blood plasma levels of lithium were found to be comparable to low-moderate human therapeutic levels. These data confirm the viability and utility of ketamine-induced hyperlocomotion as a rodent model of mania.

Quantum indistinguishability in chemical reactions.

Quantum indistinguishability plays a crucial role in many low-energy physical phenomena, from quantum fluids to molecular spectroscopy. It is, however, typically ignored in most high-temperature processes, particularly for ionic coordinates, implicitly assumed to be distinguishable, incoherent, and thus well approximated classically. We explore enzymatic chemical reactions involving small symmetric molecules and argue that in many situations a full quantum treatment of collective nuclear degrees of freedom is essential. Supported by several physical arguments, we conjecture a "quantum dynamical selection" (QDS) rule for small symmetric molecules that precludes chemical processes that involve direct transitions from orbitally nonsymmetric molecular states. As we propose and discuss, the implications of the QDS rule include (i) a differential chemical reactivity of para- and orthohydrogen, (ii) a mechanism for inducing intermolecular quantum entanglement of nuclear spins, (iii) a mass-independent isotope fractionation mechanism, (iv) an explanation of the enhanced chemical activity of "reactive oxygen species", (v) illuminating the importance of ortho-water molecules in modulating the quantum dynamics of liquid water, and (vi) providing the critical quantum-to-biochemical linkage in the nuclear spin model of the (putative) quantum brain, among others.

Posner molecules: from atomic structure to nuclear spins.

We investigate "Posner molecules", calcium phosphate clusters with chemical formula Ca9(PO4)6. Originally identified in hydroxyapatite, Posner molecules have also been observed as free-floating molecules in vitro. The formation and aggregation of Posner molecules have important implications for bone growth, and may also play a role in other biological processes such as the modulation of calcium and phosphate ion concentrations within the mitochondrial matrix. In this work, we use a first-principles computational methodology to study the structure of Posner molecules, their vibrational spectra, their interactions with other cations, and the process of pairwise bonding. Additionally, we show that the Posner molecule provides an ideal environment for the six constituent 31P nuclear spins to obtain very long spin coherence times. In vitro, the spins could provide a platform for liquid-state nuclear magnetic resonance quantum computation. In vivo, the spins may have medical imaging applications. The spins have also been suggested as "neural qubits" in a proposed mechanism for quantum processing in the brain.

Atypical energy eigenstates in the Hubbard chain and quantum disentangled liquids.

We investigate the implications of integrability for the existence of quantum disentangled liquid (QDL) states in the half-filled one-dimensional Hubbard model. We argue that there exist finite energy-density eigenstates that exhibit QDL behaviour in the sense of Grover & Fisher (2014 J. Stat. Mech.2014, P10010. (doi:10.1088/1742-5468/2014/10/P10010)). These states are atypical in the sense that their entropy density is smaller than that of thermal states at the same energy density. Furthermore, we show that thermal states in a particular temperature window exhibit a weaker form of the QDL property, in agreement with recent results obtained by strong-coupling expansion methods in Veness et al. (2016 (http://arxiv.org/abs/1611.02075)).This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.

Plaquette ordered phase and quantum phase diagram in the spin-1/2 J(1)-J(2) square Heisenberg model.

We study the spin-1/2 Heisenberg model on the square lattice with first- and second-neighbor antiferromagnetic interactions J(1) and J(2), which possesses a nonmagnetic region that has been debated for many years and might realize the interesting Z(2) spin liquid. We use the density matrix renormalization group approach with explicit implementation of SU(2) spin rotation symmetry and study the model accurately on open cylinders with different boundary conditions. With increasing J(2), we find a Néel phase and a plaquette valence-bond (PVB) phase with a finite spin gap. From the finite-size scaling of the magnetic order parameter, we estimate that the Néel order vanishes at J(2)/J(1)≃0.44. For 0.5

Non-Fermi-liquid d-wave metal phase of strongly interacting electrons.

Developing a theoretical framework for conducting electronic fluids qualitatively distinct from those described by Landau's Fermi-liquid theory is of central importance to many outstanding problems in condensed matter physics. One such problem is that, above the transition temperature and near optimal doping, high-transition-temperature copper-oxide superconductors exhibit 'strange metal' behaviour that is inconsistent with being a traditional Landau Fermi liquid. Indeed, a microscopic theory of a strange-metal quantum phase could shed new light on the interesting low-temperature behaviour in the pseudogap regime and on the d-wave superconductor itself. Here we present a theory for a specific example of a strange metal--the 'd-wave metal'. Using variational wavefunctions, gauge theoretic arguments, and ultimately large-scale density matrix renormalization group calculations, we show that this remarkable quantum phase is the ground state of a reasonable microscopic Hamiltonian--the usual t-J model with electron kinetic energy t and two-spin exchange J supplemented with a frustrated electron 'ring-exchange' term, which we here examine extensively on the square lattice two-leg ladder. These findings constitute an explicit theoretical example of a genuine non-Fermi-liquid metal existing as the ground state of a realistic model.

Spin liquid phases for spin-1 systems on the triangular lattice.

Motivated by recent experiments on material Ba3NiSb2O9, we propose two novel spin liquid phases (A and B) for spin-1 systems on a triangular lattice. At the mean field level, both spin liquid phases have gapless fermionic spinon excitations with quadratic band touching; thus, in both phases the spin susceptibility and γ=C(v)/T saturate to a constant at zero temperature, which are consistent with the experimental results on Ba3NiSb2O9. On the lattice scale, these spin liquid phases have Sp(4)~SO(5) gauge fluctuation, while in the long wavelength limit this Sp(4) gauge symmetry is broken down to U(1)×Z(2) in the type A spin liquid phase, and broken down to Z(4) in the type B phase. We also demonstrate that the A phase is the parent state of the ferroquadrupole state, nematic state, and the noncollinear spin density wave state.

Spin Bose-metal and valence bond solid phases in a spin-1/2 model with ring exchanges on a four-leg triangular ladder.

We study a spin-1/2 system with Heisenberg plus ring exchanges on a four-leg triangular ladder using the density matrix renormalization group and Gutzwiller variational wave functions. Near an isotropic lattice regime, for moderate to large ring exchanges we find a spin Bose-metal phase with a spinon Fermi sea consisting of three partially filled bands. Going away from the triangular towards the square lattice regime, we find a staggered dimer phase with dimers in the transverse direction, while for small ring exchanges the system is in a featureless rung phase. We also discuss parent states and a possible phase diagram in two dimensions.

Exotic gapless mott insulators of bosons on multileg ladders.

We present evidence for an exotic gapless insulating phase of hard-core bosons on multileg ladders with a density commensurate with the number of legs. In particular, we study in detail a model of bosons moving with direct hopping and frustrating ring exchange on a 3-leg ladder at ν=1/3 filling. For sufficiently large ring exchange, the system is insulating along the ladder but has two gapless modes and power law transverse density correlations at incommensurate wave vectors. We propose a determinantal wave function for this phase and find excellent comparison between variational Monte Carlo and density matrix renormalization group calculations on the model Hamiltonian, thus providing strong evidence for the existence of this exotic phase. Finally, we discuss extensions of our results to other N-leg systems and to N-layer two-dimensional structures.

Exotic paired states with anisotropic spin-dependent Fermi surfaces.

We propose a model for realizing exotic paired states in cold Fermi gases by using a spin-dependent optical lattice to engineer mismatched Fermi surfaces for each hyperfine species. The BCS phase diagram shows a stable paired superfluid state with coexisting pockets of momentum space with gapless unpaired carriers, similar to the Sarma state in polarized mixtures, but in our case the system is unpolarized. We propose the possible existence of an exotic "Cooper-pair Bose-metal" phase, which has a gap for single fermion excitations but gapless and uncondensed "Cooper-pair" excitations residing on a "Bose surface" in momentum space.

Interlayer coherent composite Fermi liquid phase in quantum Hall bilayers.

We introduce an interlayer coherent composite Fermi liquid for nu = 1/2 + 1/2 bilayers, in which interlayer Coulomb repulsion drives exciton condensation of composite fermions. As a result, composite fermions propagate coherently between layers--even though electrons do not--and form bonding and antibonding Fermi seas. This phase is compressible with respect to symmetric currents but quantum Hall-like in the counterflow channel. Quantum oscillations of the composite Fermi seas generate a new series of incompressible states at nu = p/[2(p +/- 1)] per layer (p an integer), which is a bilayer analogue of Jain's sequence.

Nonequilibrium transport through a point contact in the nu = 5/2 non-Abelian quantum Hall state.

We analyze charge-e/4 quasiparticle tunneling between the edges of a point contact in a non-Abelian model of the nu = 5/2 quantum Hall state in the presence of a finite voltage difference using the time-dependent density-matrix renormalization group method. We confirm that, as the voltage decreases, the system is broken into two pieces. In the limits of small and large voltage, we recover the results expected from perturbation theory about the infrared and ultraviolet fixed points. We test our methods by finding the analogous nonequilibrium current through a point contact at nu = 1/3.

Universal periods in quantum Hall droplets.

Using the hierarchy picture of the fractional quantum Hall effect, we study the ground-state periodicity of a finite size quantum Hall droplet in a quantum Hall fluid of a different filling factor. The droplet edge charge is periodically modulated with flux through the droplet and will lead to a periodic variation in the conductance of a nearby point contact, such as occurs in some quantum Hall interferometers. Our model is consistent with experiment and predicts that superperiods can be observed in geometries where no interfering trajectories occur. The model may also provide an experimentally feasible method of detecting elusive neutral modes and otherwise obtaining information about the microscopic edge structure in fractional quantum Hall states.