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arXiv:2405.18477 · Physical Review Research

Finite-temperature Rydberg arrays: Quantum phases and entanglement characterization

Nora Reinić, Daniel Jaschke, Darvin Wanisch, Pietro Silvi, Simone Montangero

Published Sep 20, 2024• 5 citations
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Abstract

As one of the most prominent platforms for analog quantum simulators, Rydberg atom arrays are a promising tool for exploring quantum phases and transitions. While the ground-state properties of one-dimensional Rydberg systems are already thoroughly examined, we extend the analysis towards the finite-temperature scenario. For this purpose, we develop a tensor network-based numerical toolbox for constructing the quantum many-body states at thermal equilibrium, which we exploit to probe classical correlations as well as entanglement monotones. We clearly observe ordered phases continuously shrinking because of thermal fluctuations at finite system sizes. Moreover, by examining the entanglement of formation and entanglement negativity of a half-system bipartition, we numerically confirm that a conformal scaling law of entanglement extends from the zero-temperature critical points into the low-temperature regime. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.033322

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As one of the most prominent platforms for analog quantum simulators, Rydberg atom arrays are a promising tool for exploring quantum phases and transitions. While the ground-state properties of one-dimensional Rydberg systems are already thoroughly examined, we extend the analysis towards the finite-temperature scenario. For this purpose, we develop a tensor network-based numerical toolbox for constructing the quantum many-body states at thermal equilibrium, which we exploit to probe classical correlations as well as entanglement monotones. We clearly observe ordered phases continuously shrinking because of thermal fluctuations at finite system sizes. Moreover, by examining the entanglement of formation and entanglement negativity of a half-system bipartition, we numerically confirm that a conformal scaling law of entanglement extends from the zero-temperature critical points into the low-temperature regime. Published by the American Physical Society 2024
Rydberg atom arrays have emerged as a powerful platform for experimental research and a challenging subject for theoretical investigation in quantum science. In this study, we investigate the finite-temperature properties of two-dimensional square-lattice Rydberg atom arrays using the projected entangled pair states (PEPS) method. By analyzing the thermal behavior of systems in the checkerboard and striated phases, we extract critical exponents and identify phase transition characteristics. Our results confirm that the checkerboard phase transition belongs to the 2D Ising universality class, while the striated phase exhibits critical exponents that deviate from known universality classes, possibly due to finite-size effects. These findings provide theoretical insights into the thermal stability of quantum phases in Rydberg atom arrays and offer valuable guidance for future experimental efforts.
Recent experimental advances have stimulated interest in the use of large, two-dimensional arrays of Rydberg atoms as a platform for quantum information processing and to study exotic many-body quantum states. However, the native long-range interactions between the atoms complicate experimental analysis and precise theoretical understanding of these systems. Here we use new tensor network algorithms capable of including all long-range interactions to study the ground state phase diagram of Rydberg atoms in a geometrically unfrustrated square lattice array. We find a greatly altered phase diagram from earlier numerical and experimental studies, revealed by studying the phases on the bulk lattice and their analogs in experiment-sized finite arrays. We further describe a previously unknown region with a nematic phase stabilized by short-range entanglement and an order from disorder mechanism. Broadly our results yield a conceptual guide for future experiments, while our techniques provide a blueprint for converging numerical studies in other lattices.
Dual-species Rydberg atom arrays extend single-species platforms by introducing competing interaction scales and enhanced quantum fluctuations, enabling phenomena beyond homogeneous settings. In this work, we study the ground-state phase diagram of a one-dimensional dual-species Rydberg atom ladder using large-scale density-matrix renormalization group calculations. We identify disordered phases, multiple ordered phases with Z2\mathbb{Z}_2Z2​, Z3\mathbb{Z}_3Z3​, and Z4\mathbb{Z}_4Z4​ symmetry, as well as floating phases characterized by incommensurate wave vectors and algebraically decaying correlations. Importantly, we observe a smooth crossover between distinct Z2\mathbb{Z}_2Z2​-ordered regimes, reflecting a reorganization of low-energy degrees of freedom rather than a true phase transition, which is absent in single-species Rydberg arrays. We further uncover a multi-critical point at the boundary between the Z2⊗Z2\mathbb{Z}_2 \otimes \mathbb{Z}_2Z2​⊗Z2​ and Z3⊗Z3\mathbb{Z}_3 \otimes \mathbb{Z}_3Z3​⊗Z3​ ordered phases, where Ising, chiral, and first-order transition lines intersect. Our results demonstrate that dual-species Rydberg atom arrays provide a unique platform for realizing crossover physics and multi-critical behavior inaccessible in single-species architectures.
Arrays of ultracold neutral atoms, also known as Rydberg atom arrays, are rapidly developing into a powerful and versatile platform for quantum simulation. However, theoretical predictions about the bulk quantum phases of matter present in these systems have often diverged from experimental realizations on finite-sized arrays due to the strong effects of the boundaries. Here we propose a general, experimentally straightforward strategy to mitigate the effects of the boundaries and thus enable finite-sized arrays to stabilize bulk-like quantum order. Our scheme makes use of the properties of the ubiquitous disordered phase in Rydberg systems, driving the boundaries into an unbiased set of configurations that depend on the bulk physics. We numerically demonstrate the efficacy of this protocol in one- and two-dimensional systems on both ordered and critical phases.
Synthetic-dimension platforms offer unique pathways for engineering quantum matter. We compute the phase diagram of a many-body system of ultracold atoms (or polar molecules) with a set of Rydberg states (or rotational states) as a synthetic dimension, where the particles are arranged in real space in optical microtrap arrays and interact via dipole-dipole exchange interaction. Using mean-field theory, we find three ordered phases---two are localized in the synthetic dimension, predicted as zero-temperature ground states by Sundar et al. [Sci. Rep. 8, 3422 (2018); Phys. Rev. A 99, 013624 (2019)], and one is a delocalized phase. We characterize them by identifying the spontaneously broken discrete symmetries of the Hamiltonian. We also compute the phase diagram as a function of temperature and interaction strength for both signs of the interaction. For system sizes with more than six synthetic sites and attractive interactions, we find that the thermal phase transitions can be first or second order, which leads to a tricritical point on the phase boundary. By examining the dependence of the tricritical point and other special points of the phase boundary on the synthetic dimension size, we shed light on the physics for thermodynamically large synthetic dimension.
At the interface of quantum information and condensed matter physics, the study of entanglement in quantum many-body systems requires a new toolset which combines concepts from each. This thesis introduces a set of computational methods to study phases and phase transitions in lattice models of quantum systems, using the Renyi entropies as a means of quantifying entanglement. The scaling of entanglement entropy can give valuable insight into the phase of a condensed matter system. It can be used to detect exotic types of phases, to pinpoint transitions between phases, and can give us universal information about a system. \nThe first approach in this thesis is a technique to measure entanglement in finite size \nlattice systems using zero-temperature quantum Monte Carlo simulations. The algorithm \nis developed, implemented, and used to explore anomalous entanglement scaling terms in \nthe spin-1/2 Heisenberg antiferromagnet. \nIn the second part of this thesis, a new and complementary numerical technique is introduced to study entanglement not just in finite size systems, but as we approach the thermodynamic limit. This “numerical linked-cluster expansion” is used to study two different systems at their quantum critical points — continuous phase transitions occurring at zero temperature, at which these systems exhibit universal properties. Remarkably, these universal properties can be reflected in the scaling of entanglement. \nEntanglement offers a new perspective on condensed matter systems, one which takes us closer to genuinely understanding what goes on in these materials at the quantum mechanical level. This thesis demonstrates the first steps in developing an extensive list of computational tools that can be used to study entanglement over a wide range of interacting quantum many-body systems. With the ever increasing computational power available, it may be only a matter of time before these tools are used to create a comprehensive framework for the characterization of condensed matter phases and phase transitions.