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1. Walking with the Atoms in a Chemical Bond: A Perspective Using Quantum Phase Transition

   https://doi.org/10.3390/e26030230  

   Kais, Sabre (March 2024, Entropy)

   Phase transitions happen at critical values of the controlling parameters, such as the critical temperature in classical phase transitions, and system critical parameters in the quantum case. However, true criticality happens only at the thermodynamic limit, when the number of particles goes to infinity with constant density. To perform the calculations for the critical parameters, a finite-size scaling approach was developed to extrapolate information from a finite system to the thermodynamic limit. With the advancement in the experimental and theoretical work in the field of ultra-cold systems, particularly trapping and controlling single atomic and molecular systems, one can ask: do finite systems exhibit quantum phase transition? To address this question, finite-size scaling for finite systems was developed to calculate the quantum critical parameters. The recent observation of a quantum phase transition in a single trapped 171 Yb+ ion indicates the possibility of quantum phase transitions in finite systems. This perspective focuses on examining chemical processes at ultra-cold temperatures, as quantum phase transitions—particularly the formation and dissociation of chemical bonds—are the basic processes for understanding the whole of chemistry. 

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2. Observation of measurement-induced quantum phases in a trapped-ion quantum computer

   Crystal Noel, Pradeep Niroula (January 2021, ArXivorg)

   Many-body open quantum systems balance internal dynamics against decoherence from interactions with an environment. Here, we explore this balance via random quantum circuits implemented on a trapped ion quantum computer, where the system evolution is represented by unitary gates with interspersed projective measurements. As the measurement rate is varied, a purification phase transition is predicted to emerge at a critical point akin to a fault-tolerent threshold. We probe the "pure" phase, where the system is rapidly projected to a deterministic state conditioned on the measurement outcomes, and the "mixed" or "coding" phase, where the initial state becomes partially encoded into a quantum error correcting codespace. We find convincing evidence of the two phases and show numerically that, with modest system scaling, critical properties of the transition clearly emerge. 

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3. Critical fluctuations in a confined driven-dissipative quantum condensate

   https://doi.org/10.1126/sciadv.adi6762  

   Alnatah, Hassan; Comaron, Paolo; Mukherjee, Shouvik; Beaumariage, Jonathan; Pfeiffer, Loren N; West, Ken; Baldwin, Kirk; Szymańska, Marzena; Snoke, David W (March 2024, Science Advances)

   Phase fluctuations determine the low-energy properties of quantum condensates. However, at the condensation threshold, both density and phase fluctuations are relevant. While strong emphasis has been given to the investigation of phase fluctuations, which dominate the physics of the quantum system away from the critical point, number fluctuations have been much less explored even in thermal equilibrium. In this work, we report experimental observation and theoretical description of fluctuations in a circularly confined nonequilibrium Bose-Einstein condensate of polaritons near the condensation threshold. We observe critical fluctuations, which combine the number fluctuations of a single-mode condensate state and competition between different states. The latter is analogous to mode hopping in photon lasers. Our theoretical analysis indicates that this phenomenon is of a quantum character, while classical noise of the pump is not sufficient to explain the experiments. The manifestation of a critical quantum state competition unlocks possibilities for the study of condensate formation while linking to practical realizations in photonic lasers. 

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4. Detecting Quantum Critical Points of Correlated Systems by Quantum Convolutional Neural Network Using Data from Variational Quantum Eigensolver

   https://doi.org/10.3390/quantum4040042  

   Wrobel, Nathaniel; Baul, Anshumitra; Tam, Ka-Ming; Moreno, Juana (December 2022, Quantum Reports)

   Machine learning has been applied to a wide variety of models, from classical statistical mechanics to quantum strongly correlated systems, for classifying phase transitions. The recently proposed quantum convolutional neural network (QCNN) provides a new framework for using quantum circuits instead of classical neural networks as the backbone of classification methods. We present the results from training the QCNN by the wavefunctions of the variational quantum eigensolver for the one-dimensional transverse field Ising model (TFIM). We demonstrate that the QCNN identifies wavefunctions corresponding to the paramagnetic and ferromagnetic phases of the TFIM with reasonable accuracy. The QCNN can be trained to predict the corresponding ‘phase’ of wavefunctions around the putative quantum critical point even though it is trained by wavefunctions far away. The paper provides a basis for exploiting the QCNN to identify the quantum critical point. 

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5. Strain-tuned topological phase transition and unconventional Zeeman effect in ZrTe5 microcrystals

   https://doi.org/10.1038/s43246-022-00316-5  

   Gaikwad, Apurva; Sun, Song; Wang, Peipei; Zhang, Liyuan; Cano, Jennifer; Dai, Xi; Du, Xu (November 2022, Communications Materials)

   Abstract The geometric phase of an electronic wave function, also known as Berry phase, is the fundamental basis of the topological properties in solids. This phase can be tuned by modulating the band structure of a material, providing a way to drive a topological phase transition. However, despite significant efforts in designing and understanding topological materials, it remains still challenging to tune a given material across different topological phases while tracing the impact of the Berry phase on its quantum transport properties. Here, we report these two effects in a magnetotransport study of ZrTe₅. By tuning the band structure with uniaxial strain, we use quantum oscillations to directly map a weak-to-strong topological insulator phase transition through a gapless Dirac semimetal phase. Moreover, we demonstrate the impact of the strain-tunable spin-dependent Berry phase on the Zeeman effect through the amplitude of the quantum oscillations. We show that such a spin-dependent Berry phase, largely neglected in solid-state systems, is critical in modeling quantum oscillations in Dirac bands of topological materials. 

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