In recent years, dynamical phase transitions and out-of-equilibrium criticality have been at the forefront of ultracold gases and condensed matter research. Whereas universality and scaling are established topics in equilibrium quantum many-body phys
ics, out-of-equilibrium extensions of such concepts still leave much to be desired. Using exact diagonalization and the time-dependent variational principle in uniform martrix product states, we calculate the time evolution of the local order parameter and Loschmidt return rate in transverse-field Ising chains with antiferromagnetic power law-decaying interactions, and map out the corresponding rich dynamical phase diagram. textit{Anomalous} cusps in the return rate, which are ubiquitous at small quenches within the ordered phase in the case of ferromagnetic long-range interactions, are absent within the accessible timescales of our simulations. We attribute this to much weaker domain-wall binding in the antiferromagnetic case. For quenches across the quantum critical point, textit{regular} cusps appear in the return rate and connect to the local order parameter changing sign, indicating the concurrence of two major concepts of dynamical phase transitions. Our results consolidate conclusions of previous works that a necessary condition for the appearance of anomalous cusps in the return rate after quenches within the ordered phase is for topologically trivial local spin flips to be the energetically dominant excitations in the spectrum of the quench Hamiltonian. Our findings are readily accessible in modern trapped-ion setups, and we outline the associated experimental considerations.
The solution of gauge theories is one of the most promising applications of quantum technologies. Here, we discuss the approach to the continuum limit for $U(1)$ gauge theories regularized via finite-dimensional Hilbert spaces of quantum spin-$S$ ope
rators, known as quantum link models. For quantum electrodynamics (QED) in one spatial dimension, we numerically demonstrate the continuum limit by extrapolating the ground state energy, the scalar, and the vector meson masses to large spin lengths $S$, large volume $N$, and vanishing lattice spacing $a$. By analytically solving Gauss law for arbitrary $S$, we obtain a generalized PXP spin model and count the physical Hilbert space dimension analytically. This allows us to quantify the required resources for reliable extrapolations to the continuum limit on quantum devices. We use a functional integral approach to relate the model with large values of half-integer spins to the physics at topological angle $Theta=pi$. Our findings indicate that quantum devices will in the foreseeable future be able to quantitatively probe the QED regime with quantum link models.
Based on the MPS formalism, we introduce an ansatz for capturing excited states in finite systems with open boundary conditions, providing a very efficient method for computing, e.g., the spectral gap of quantum spin chains. This method can be straig
htforwardly implemented on top of an existing DMRG or MPS ground-state code. Although this approach is built on open-boundary MPS, we also apply it to systems with periodic boundary conditions. Despite the explicit breaking of translation symmetry by the MPS representation, we show that momentum emerges as a good quantum number, and can be exploited for labeling excitations on top of MPS ground states. We apply our method to the critical Ising chain on a ring and the classical Potts model on a cylinder. Finally, we apply the same idea to compute excitation spectra for 2-D quantum systems on infinite cylinders. Again, despite the explicit breaking of translation symmetry in the periodic direction, we recover momentum as a good quantum number for labeling excitations. We apply this method to the 2-D transverse-field Ising model and the half-filled Hubbard model; for the latter, we obtain accurate results for, e.g., the hole dispersion for cylinder circumferences up to eight sites.
In recent years, dynamical quantum phase transitions (DQPTs) have emerged as a useful theoretical concept to characterize nonequilibrium states of quantum matter. DQPTs are marked by singular behavior in an textit{effective free energy} $lambda(t)$,
which, however, is a global measure, making its experimental or theoretical detection challenging in general. We introduce two local measures for the detection of DQPTs with the advantage of requiring fewer resources than the full effective free energy. The first, called the textit{real-local} effective free energy $lambda_M(t)$, is defined in real space and is therefore suitable for systems where locally resolved measurements are directly accessible such as in quantum-simulator experiments involving Rydberg atoms or trapped ions. We test $lambda_M(t)$ in Ising chains with nearest-neighbor and power-law interactions, and find that this measure allows extraction of the universal critical behavior of DQPTs. The second measure we introduce is the textit{momentum-local} effective free energy $lambda_k(t)$, which is targeted at systems where momentum-resolved quantities are more naturally accessible, such as through time-of-flight measurements in ultracold atoms. We benchmark $lambda_k(t)$ for the Kitaev chain, a paradigmatic system for topological quantum matter, in the presence of weak interactions. Our introduced local measures for effective free energies can further facilitate the detection of DQPTs in modern quantum-simulator experiments.
A central primitive in quantum tensor network simulations is the problem of approximating a matrix product state with one of a lower bond dimension. This problem forms the central bottleneck in algorithms for time evolution and for contracting projec
ted entangled pair states. We formulate a tangent-space based variational algorithm to achieve this for uniform (infinite) matrix product states. The algorithm exhibits a favourable scaling of the computational cost, and we demonstrate its usefulness by several examples involving the multiplication of a matrix product state with a matrix product operator.
Considering nonintegrable quantum Ising chains with exponentially decaying interactions, we present matrix product state results that establish a connection between low-energy quasiparticle excitations and the kind of nonanalyticities in the Loschmid
t return rate. When domain walls in the spectrum of the quench Hamiltonian are energetically favored to be bound rather than freely propagating, anomalous cusps appear in the return rate regardless of the initial state. In the nearest-neighbor limit, domain walls are always freely propagating, and anomalous cusps never appear. As a consequence, our work illustrates that models in the same equilibrium universality class can still exhibit fundamentally distinct out-of-equilibrium criticality. Our results are accessible to current ultracold-atom and ion-trap experiments.
