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arXiv:1403.4066 · Europhysics Letters (EPL)

Observing a quantum phase transition by measuring a single spin

Manuel Gessner, Michael T. Ramm, Hartmut Häffner, Andreas Buchleitner, Heinz‐Peter Breuer

Published Aug 1, 2014• 24 citations
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Abstract

We show that the ground-state quantum correlations of an Ising model can be detected by monitoring the time evolution of a single spin alone, and that the critical point of a quantum phase transition is detected through a maximum of a suitably defined observable. A proposed implementation with trapped ions realizes an experimental probe of quantum phase transitions which is based on quantum correlations and scalable for large system sizes.

DOI
10.1209/0295-5075/107/40005

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We show that the ground-state quantum correlations of an Ising model can be detected by monitoring the time evolution of a single spin alone, and that the critical point of a quantum phase transition is detected through a maximum of a suitably defined observable. A proposed implementation with trapped ions realizes an experimental probe of quantum phase transitions which is based on quantum correlations and scalable for large system sizes.
The study of quantum phase transitions requires the preparation of a many-body system near its ground state, a challenging task for many experimental systems. The measurement of quench dynamics, on the other hand, is now a routine practice in most cold atom platforms. Here we show that quintessential ingredients of quantum phase transitions can be probed directly with quench dynamics in integrable and nearly integrable systems. As a paradigmatic example, we study global quench dynamics in a transverse-field Ising model with either short-range or long-range interactions. When the model is integrable, we discover a new dynamical critical point with a nonanalytic signature in the short-range correlators. The location of the dynamical critical point matches that of the quantum critical point and can be identified using a finite-time scaling method. We extend this scaling picture to systems near integrability and demonstrate the continued existence of a dynamical critical point detectable at prethermal timescales. We quantify the difference in the locations of the dynamical and quantum critical points away from (but near) integrability. Thus, we demonstrate that this method can be used to approximately locate the quantum critical point near integrability. The scaling method is also relevant to experiments with finite time and system size, and our predictions are testable in near-term experiments with trapped ions and Rydberg atoms.
We introduce observable quantities, borrowing from concepts of quantum information theory, for the characterization of quantum phase transitions in spin systems. These observables are uniquely defined in terms of single spin unitary operations. We define the energy gap between the ground state and the state produced by the action of a single-qubit local gate. We show that this static quantity involves only single-site expectations and two-point correlation functions on the ground state. We then discuss a dynamical local observable defined as the acceleration of quantum state evolution after performing an instaneous single-qubit perturbation on the ground state. This quantity involves three-point correlations as well. We show that both the static and the dynamical observables detect and characterize completely quantum critical points in a class of spin systems.
Quantum phase transitions occur when the ground state of a quantum system undergoes a qualitative change when an external control parameter reaches a critical value. Here, we demonstrate a technique for studying quantum systems undergoing a phase transition by coupling the system to a probe qubit. It uses directly the increased sensibility of the quantum system to perturbations when it is close to a critical point. Using an NMR quantum simulator, we demonstrate this measurement technique for two different types of quantum phase transitions in an Ising spin chain.
Out-of-time-ordered (OTO) correlators have developed into a central concept quantifying quantum information transport, information scrambling, and quantum chaos. In this Letter, we show that such an OTO correlator can also be used to dynamically detect equilibrium as well as nonequilibrium phase transitions in Ising chains. We study OTO correlators of an order parameter both in equilibrium and after a quantum quench for different variants of transverse-field Ising models in one dimension, including the integrable one as well as nonintegrable and long-range extensions. We find for all the studied models that the OTO correlator in ground states detects the quantum phase transition. After a quantum quench from a fully polarized state, we observe numerically for the short-range models that the asymptotic long-time value of the OTO correlator signals still the equilibrium critical points and ordered phases. For the long-range extension, the OTO correlator instead determines a dynamical quantum phase transition in the model. We discuss how our findings can be observed in current experiments of trapped ions or Rydberg atoms.
In the present paper we introduce a way of identifying quantum phase transitions of many-body systems by means of local time correlations and Leggett-Garg inequalities. This procedure allows us to experimentally determine the quantum critical points not only of finite-order transitions but also those of infinite order, as the Kosterlitz-Thouless transition that is not always easy to detect with current methods. By means of simple analytical arguments for a general spin-1/21/21/2 Hamiltonian, and matrix product simulations of one-dimensional XXZXXZXXZ and anisotropic XYXYXY models, we argue that finite-order quantum phase transitions can be determined by singularities of the time correlations or their derivatives at criticality. The same features are exhibited by corresponding Leggett-Garg functions, which noticeably indicate violation of the Leggett-Garg inequalities for early times and all the Hamiltonian parameters considered. In addition, we find that the infinite-order transition of the XXZXXZXXZ model at the isotropic point can be revealed by the maximal violation of the Leggett-Garg inequalities. We thus show that quantum phase transitions can be identified by purely local measurements and that many-body systems constitute important candidates to observe experimentally the violation of Leggett-Garg inequalities.
During a quantum measurement, superpositions of states with different observable properties probabilistically collapse into one with a sharp value of the measured observable. In macroscopic quantum systems, this collapse arises via a continuous measurement-induced phase transition (MIPT) at a critical value of the strength of interaction with the measurement apparatus. MIPTs lie outside established paradigms for equilibrium or nonequilibrium critical phenomena and delineate distinct, stable dynamical and computational phases of matter. Quantum computers enable programmable simulation of the interaction of a measurement apparatus with a dynamical quantum system, to explore MIPT phenomena over a range of system sizes while retaining quantum coherence. Yet, existing experimental protocols rely on fundamentally nonscalable postselection techniques or direct classical simulation of quantum circuits. Here, we report the scalable observation of finite-size scaling evidence for an observable-sharpening MIPT in monitored quantum circuits in a chain of Yb + 171 ions in Quantinuum’s H1-1 trapped-ion quantum processor. By leveraging an equivalent description as a statistical physics problem, we implement scalable classical algorithms to infer the value of the measured observable from a single experimental shot. This technique enables a truly scalable protocol to observe observable-sharpening MIPTs in generic classes of circuits that cannot be directly classically simulated and also provides enhanced means to detect and suppress errors in the quantum simulation. Published by the American Physical Society 2024