Search Results
Observation of orbital order in the van der Waals material 1T−TiSe2
2022, Peng, Yingying, Guo, Xuefei, Xiao, Qian, Li, Qizhi, Strempfer, Jörg, Choi, Yongseong, Yan, Dong, Luo, Huixia, Huang, Yuqing, Jia, Shuang, Janson, Oleg, Abbamonte, Peter, van den Brink, Jeroen, van Wezel, Jasper
Besides magnetic and charge order, regular arrangements of orbital occupation constitute a fundamental order parameter of condensed matter physics. Even though orbital order is difficult to identify directly in experiments, its presence was firmly established in a number of strongly correlated, three-dimensional Mott insulators. Here, reporting resonant x-ray-scattering experiments on the layered van der Waals compound 1T-TiSe2, we establish that the known charge density wave in this weakly correlated, quasi-two-dimensional material corresponds to an orbital ordered phase. Our experimental scattering results are consistent with first-principles calculations that bring to the fore a generic mechanism of close interplay between charge redistribution, lattice displacements, and orbital order. It demonstrates the essential role that orbital degrees of freedom play in TiSe2, and their importance throughout the family of correlated van der Waals materials.
Horizon physics of quasi-one-dimensional tilted Weyl cones on a lattice
2022, Könye, Viktor, Morice, Corentin, Chernyavsky, Dmitry, Moghaddam, Ali G., van den Brink, Jeroen, van Wezel, Jasper
To simulate the dynamics of massless Dirac fermions in curved space-times with one, two, and three spatial dimensions, we construct tight-binding Hamiltonians with spatially varying hoppings. These models represent tilted Weyl semimetals where the tilting varies with position, in a manner similar to the light cones near the horizon of a black hole. We illustrate the gravitational analogies in these models by numerically evaluating the propagation of wave packets on the lattice and then comparing them to the geodesics of the corresponding curved space-time. We also show that the motion of electrons in these spatially varying systems can be understood through the conservation of energy and the quasiconservation of quasimomentum. This picture is confirmed by calculations of the scattering matrix, which indicate an exponential suppression of any noncontinuous change in the quasimomentum. Finally, we show that horizons in the lattice models can be constructed also at finite energies using specially designed tilting profiles.
Stochastic field dynamics in models of spontaneous unitarity violation
2024, Mertens, Lotte, Wesseling, Matthijs, van Wezel, Jasper
Objective collapse theories propose a solution to the quantum measurement problem by predicting deviations from Schrödinger's equation that can be tested experimentally. A class of objective theories based on spontaneous unitarity violation was recently introduced, in which the stochastic field required for obtaining Born's rule does not depend on the state of the system being measured. Here, we classify possible models for the stochastic field dynamics in theories of spontaneous unitarity violation. We show that for correlated stochastic dynamics, the field must be defined on a closed manifold. In two or more dimensions, it is then always possible to find stochastic dynamics yielding Born's rule, independent of the state being measured or the correlation time of the stochastic field. We show that the models defined this way are all isomorphic to the definition on a two-sphere, which we propose to be a minimal physical model for the stochastic field in models of spontaneous unitarity violation.
Environment-Assisted Invariance Does Not Necessitate Born’s Rule for Quantum Measurement
2023, Mertens, Lotte, van Wezel, Jasper
The argument of environment-assisted invariance (known as envariance) implying Born’s rule is widely used in models for quantum measurement to reason that they must yield the correct statistics, specifically for linear models. However, it has recently been shown that linear collapse models can never give rise to Born’s rule. Here, we address this apparent contradiction and point out an inconsistency in the assumptions underlying the arguments based on envariance. We use a construction in which the role of the measurement machine is made explicit and shows that the presence of envariance does not imply that every measurement will behave according to Born’s rule. Rather, it implies that every quantum state allows a measurement machine to be constructed, which yields Born’s rule when measuring that particular state. This resolves the paradox and is in agreement with the recent result of objective collapse models necessarily being nonlinear.
Engineering spectral properties of non-interacting lattice Hamiltonians
2021, Moghaddam, Ali G., Chernyavsky, Dmitry, Morice, Corentin, van Wezel, Jasper, van den Brink, Jeroen
We investigate the spectral properties of one-dimensional lattices with position-dependent hopping amplitudes and on-site potentials that are smooth bounded functions of the position. We find an exact integral form for the density of states (DOS) in the limit of an infinite number of sites, which we derive using a mixed Bloch-Wannier basis consisting of piecewise Wannier functions. Next, we provide an exact solution for the inverse problem of constructing the position-dependence of hopping in a lattice model yielding a given DOS. We confirm analytic results by comparing them to numerics obtained by exact diagonalization for various incarnations of position-dependent hoppings and on-site potentials. Finally, we generalize the DOS integral form to multi-orbital tight-binding models with longer-range hoppings and in higher dimensions.
Thermalization by a synthetic horizon
2022, Mertens, Lotte, Moghaddam, Ali G., Chernyavsky, Dmitry, Morice, Corentin, van den Brink, Jeroen, van Wezel, Jasper
Synthetic horizons in models for quantum matter provide an alternative route to explore fundamental questions of modern gravitational theory. Here we apply these concepts to the problem of emergence of thermal quantum states in the presence of a horizon, by studying ground-state thermalization due to instantaneous horizon creation in a gravitational setting and its condensed matter analog. By a sudden quench to position-dependent hopping amplitudes in a one-dimensional lattice model, we establish the emergence of a thermal state accompanying the formation of a synthetic horizon. The resulting temperature for long chains is shown to be identical to the corresponding Unruh temperature, provided that the postquench Hamiltonian matches the entanglement Hamiltonian of the prequench system. Based on detailed analysis of the outgoing radiation we formulate the conditions required for the synthetic horizon to behave as a purely thermal source, paving a way to explore this interplay of quantum-mechanical and gravitational aspects experimentally.
Quantum dynamics in 1D lattice models with synthetic horizons
2022, Morice, Corentin, Chernyavsky, Dmitry, van Wezel, Jasper, van den Brink, Jeroen, Moghaddam, Ali
We investigate the wave packet dynamics and eigenstate localization in recently proposed generalized lattice models whose low-energy dynamics mimics a quantum field theory in (1+1)D curved spacetime with the aim of creating systems analogous to black holes. We identify a critical slowdown of zero-energy wave packets in a family of 1D tight-binding models with power-law variation of the hopping parameter, indicating the presence of a horizon. Remarkably, wave packets with non-zero energies bounce back and reverse direction before reaching the horizon. We additionally observe a power-law localization of all eigenstates, each bordering a region of exponential suppression. These forbidden regions dictate the closest possible approach to the horizon of states with any given energy. These numerical findings are supported by a semiclassical description of the wave packet trajectories, which are shown to coincide with the geodesics expected for the effective metric emerging from the considered lattice models in the continuum limit.