Superfluid density and quasi-long-range order in the one-dimensional disordered Bose-Hubbard model

We study the equilibrium properties of the one-dimensional disordered Bose-Hubbard model by means of a gauge-adaptive tree tensor network variational method suitable for systems with periodic boundary conditions. We compute the superfluid stiffness and superfluid correlations close to the superfluid to glass transition line, obtaining accurate locations of the critical points. By studying the statistics of the exponent of the power-law decay of the correlation, we determine the boundary between the superfluid region and the Bose glass phase in the regime of strong disorder and in the weakly interacting region, not explored numerically before. In the former case our simulations are in agreement with previous Monte Carlo calculations.Comment: 18 pages, 12 figures; some references and two appendices added; appearing in New Journal of Physics focus issue "Strongly Interacting Quantum Gases in One Dimension

Unconstrained Tree Tensor Network: An adaptive gauge picture for enhanced performance

We introduce a variational algorithm to simulate quantum many-body states based on a tree tensor network ansatz which releases the isometry constraint usually imposed by the real-space renormalization coarse-graining: This additional numerical freedom, combined with the loop-free topology of the tree network, allows one to maximally exploit the internal gauge invariance of tensor networks, ultimately leading to a computationally flexible and efficient algorithm able to treat open and periodic boundary conditions on the same footing. We benchmark the novel approach against the 1D Ising model in transverse field with periodic boundary conditions and discuss the strategy to cope with the broken translational invariance generated by the network structure. We then perform investigations on a state-of-the-art problem, namely the bilinear-biquadratic model in the transition between dimer and ferromagnetic phases. Our results clearly display an exponentially diverging correlation length and thus support the most recent guesses on the peculiarity of the transition.Comment: 11 pages, 13 figure

The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems

We present a compendium of numerical simulation techniques, based on tensor network methods, aiming to address problems of many-body quantum mechanics on a classical computer. The core setting of this anthology are lattice problems in low spatial dimension at finite size, a physical scenario where tensor network methods, both Density Matrix Renormalization Group and beyond, have long proven to be winning strategies. Here we explore in detail the numerical frameworks and methods employed to deal with low-dimension physical setups, from a computational physics perspective. We focus on symmetries and closed-system simulations in arbitrary boundary conditions, while discussing the numerical data structures and linear algebra manipulation routines involved, which form the core libraries of any tensor network code. At a higher level, we put the spotlight on loop-free network geometries, discussing their advantages, and presenting in detail algorithms to simulate low-energy equilibrium states. Accompanied by discussions of data structures, numerical techniques and performance, this anthology serves as a programmer's companion, as well as a self-contained introduction and review of the basic and selected advanced concepts in tensor networks, including examples of their applications.Comment: 115 pages, 56 figure

Kibble-Zurek scaling of the one-dimensional Bose-Hubbard model at finite temperatures

We use tensor network methods - Matrix Product States, Tree Tensor Networks, and Locally Purified Tensor Networks - to simulate the one dimensional Bose-Hubbard model for zero and finite temperatures in experimentally accessible regimes. We first explore the effect of thermal fluctuations on the system ground state by characterizing its Mott and superfluid features. Then, we study the behavior of the out-of-equilibrium dynamics induced by quenches of the hopping parameter. We confirm a Kibble-Zurek scaling for zero temperature and characterize the finite temperature behavior, which we explain by means of a simple argument.Comment: 13 pages, 12 figure

Dynamical Ginzburg criterion for the quantum-classical crossover of the Kibble-Zurek mechanism

We introduce a simple criterion for lattice models to predict quantitatively the crossover between the classical and the quantum scaling of the Kibble-Zurek mechanism, as the one observed in a quantum $\phi^4$-model on a 1D lattice [Phys. Rev. Lett. 116, 225701 (2016)]. We corroborate that the crossover is a general feature of critical models on a lattice, by testing our paradigm on the quantum Ising model in transverse field for arbitrary spin-$s$ ($s \geq 1/2$) in one spatial dimension. By means of tensor network methods, we fully characterize the equilibrium properties of this model, and locate the quantum critical regions via our dynamical Ginzburg criterion. We numerically simulate the Kibble-Zurek quench dynamics and show the validity of our picture, also according to finite-time scaling analysis.Comment: 12 pages, 13 figure

Offloading under cognitive load: Humans are willing to offload parts of an attentionally demanding task to an algorithm.

In the near future, humans will increasingly be required to offload tasks to artificial systems to facilitate daily as well as professional activities. Yet, research has shown that humans are often averse to offloading tasks to algorithms (so-called "algorithmic aversion"). In the present study, we asked whether this aversion is also present when humans act under high cognitive load. Participants performed an attentionally demanding task (a multiple object tracking (MOT) task), which required them to track a subset of moving targets among distractors on a computer screen. Participants first performed the MOT task alone (Solo condition) and were then given the option to offload an unlimited number of targets to a computer partner (Joint condition). We found that participants significantly offloaded some (but not all) targets to the computer partner, thereby improving their individual tracking accuracy (Experiment 1). A similar tendency for offloading was observed when participants were informed beforehand that the computer partner's tracking accuracy was flawless (Experiment 2). The present findings show that humans are willing to (partially) offload task demands to an algorithm to reduce their own cognitive load. We suggest that the cognitive load of a task is an important factor to consider when evaluating human tendencies for offloading cognition onto artificial systems

Assessing fear learning via conditioned respiratory amplitude responses

Respiratory physiology is influenced by cognitive processes. It has been suggested that some cognitive states may be inferred from respiration amplitude responses (RAR) after external events. Here, we investigate whether RAR allow assessment of fear memory in cued fear conditioning, an experimental model of aversive learning. To this end, we built on a previously developed psychophysiological model (PsPM) of RAR, which regards interpolated RAR time series as the output of a linear time invariant system. We first establish that average RAR after CS+ and CS- are different. We then develop the response function of fear-conditioned RAR, to be used in our PsPM. This PsPM is inverted to yield estimates of cognitive input into the respiratory system. We analyze five validation experiments involving fear acquisition and retention, delay and trace conditioning, short and medium CS-US intervals, and data acquired with bellows and MRI-compatible pressure chest belts. In all experiments, CS+ and CS- are distinguished by their estimated cognitive inputs, and the sensitivity of this distinction is higher for model-based estimates than for peak scoring of RAR. Comparing these data with skin conductance responses (SCR) and heart period responses (HPR), we find that, on average, RAR performs similar to SCR in distinguishing CS+ and CS-, but is less sensitive than HPR. Overall, our work provides a novel and robust tool to investigate fear memory in humans that may allow wide and straightforward application to diverse experimental contexts

Inhibiting human aversive memory by transcranial theta-burst stimulation to the primary sensory cortex

BACKGROUND: Predicting adverse events from past experience is fundamental for many biological organisms. However, some individuals suffer from maladaptive memories that impair behavioral control and well-being, e.g., after psychological trauma. Inhibiting the formation and maintenance of such memories would have high clinical relevance. Previous preclinical research has focused on systemically administered pharmacological interventions, which cannot be targeted to specific neural circuits in humans. Here, we investigated the potential of noninvasive neural stimulation on the human sensory cortex in inhibiting aversive memory in a laboratory threat conditioning model. METHODS: We build on an emerging nonhuman literature suggesting that primary sensory cortices may be crucially required for threat memory formation and consolidation. Immediately before conditioning innocuous somatosensory stimuli (conditioned stimuli [CS]) to aversive electric stimulation, healthy human participants received continuous theta-burst transcranial magnetic stimulation (cTBS) to individually localized primary somatosensory cortex in either the CS-contralateral (experimental) or CS-ipsilateral (control) hemisphere. We measured fear-potentiated startle to infer threat memory retention on the next day, as well as skin conductance and pupil size during learning. RESULTS: After overnight consolidation, threat memory was attenuated in the experimental group compared with the control cTBS group. There was no evidence that this differed between simple and complex CS or that CS identifi- cation or initial learning were affected by cTBS. CONCLUSIONS: Our results suggest that cTBS to the primary sensory cortex inhibits threat memory, likely by an impact on postlearning consolidation. We propose that noninvasive targeted stimulation of the sensory cortex may provide a new avenue for interfering with aversive memories in humans