Fidelity Susceptibility Made Simple: A Unified Quantum Monte Carlo Approach

Wang, Lei; Liu, Ye-Hua; Imriška, Jakub; Nang, Ping; Troyer, Matthias

doi:10.1103/physrevx.5.031007

Cited by 86 publications

(77 citation statements)

References 107 publications

(326 reference statements)

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“…In the extreme limit of δ → 0 this is equivalent to looking at the fidelity susceptibility. This approach is well established by now [23,24]. The position of a generic continuous critical point is indicated by the peak of the fidelity susceptibility defined as the second derivative of fidelity with respect to the small shift of the external parameter.…”

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confidence: 98%

Universal shift of the fidelity susceptibility peak away from the critical point of the Berezinskii-Kosterlitz-Thouless quantum phase transition

et al. 2019

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We show that the peak which can be observed in fidelity susceptibility around the Berezinskii-Kosterlitz-Thouless transition is shifted from the quantum critical point (QCP) at Jc to J * in the gapped phase by a value |J * −Jc| = B 2 /36, where B 2 is a transition width controlling the asymptotic form of the correlation length ξ ∼ exp(−B/ |J − Jc|) in that phase. This is in contrast to the conventional continuous QCP where the maximum is an indicator of the position of the critical point. The shape of the peak is universal, emphasizing the close connection between fidelity susceptibility and the correlation length. We support those arguments with numerical matrix product state simulations of the one-dimensional Bose-Hubbard model in the thermodynamic limit, where the broad peak is located at J * = 0.212 that is significantly different from Jc = 0.3048(3). In the spin-3/2 XXZ model the shift from Jc = 1 to J * = 1.0021 is small but the narrow universal peak is much more pronounced over the non-universal background.

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confidence: 98%

Universal shift of the fidelity susceptibility peak away from the critical point of the Berezinskii-Kosterlitz-Thouless quantum phase transition

et al. 2019

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“…[31] for a review. Recently, some of us developed an efficient approach for calculating the fidelity susceptibility of quantum manybody systems [32] using modern quantum Monte Carlo (QMC) methods [33][34][35][36][37][38][39][40][41][42][43]. Specializing this to quantum impurity models, one can perform an expansion of the partition function at inverse temperature β [44]…”

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confidence: 99%

“…In the framework of Eq. (3), the fidelity susceptibility (2) can be readily calculated using a covariance estimator [32] …”

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Fidelity Susceptibility Perspective on the Kondo Effect and Impurity Quantum Phase Transitions

2015

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The Kondo effect is a ubiquitous phenomenon appearing at low temperature in quantum confined systems coupled to a continuous bath. Efforts in understanding and controlling it have triggered important developments across several disciplines of condensed matter physics. A recurring pattern in these studies is that the suppression of the Kondo effect often results in intriguing physical phenomena such as impurity quantum phase transitions or non-Fermi-liquid behavior. We show that the fidelity susceptibility is a sensitive indicator for such phenomena because it quantifies the sensitivity of the system's state with respect to its coupling to the bath. We demonstrate the power of the fidelity susceptibility approach by using it to identify the crossover and quantum phase transitions in the one and two impurity Anderson models. The feasibility of measuring fidelity susceptibility in condensed matter as well as ultracold quantum gases experiments opens exciting new routes to diagnose the Kondo problem and impurity quantum phase transitions. [7,8], and boundary conformal field theory [9] to the quantum impurity problems. Experimental interest increased in the late 1990s due to breakthroughs in fabricating artificial nanodevices [10][11][12][13][14][15]. Kondo physics is also directly relevant to dissipative two-state systems [16] and the heavy-fermion compounds [17,18]. There has also been an increasing interest in realizing the Kondo effect in ultracold atomic gases [19][20][21][22]. High controllability of the latter system may offer chances to gain even deeper understandings of the intriguing physics of quantum impurity models.A general description of the quantum impurity problems can be written aŝ HðλÞ ¼Ĥ impurity þĤ bath |fflfflfflfflfflfflfflfflfflfflffl ffl{zfflfflfflfflfflfflfflfflfflfflffl ffl}whereĤ 0 describes the quantum impurity together with a continuous bath, and the last term describes the coupling between them. We treat λ as a parameter and aim to characterize the state of the quantum impurity as a function of its coupling to the bath. The Kondo effect originates from the bath's tendency to screen the local moment formed on the quantum impurity. Renormalization group analysis shows that, in the Kondo region, the coupling strength flows to infinity at low energy [4,5], implying that the local moment will eventually get screened at a low enough temperature even with an arbitrarily weak bare impurity-bath coupling strength. There are, however, various physical processes that can compete with the Kondo effect. In the presence of such competitions, the system may undergo an impurity quantum phase transition where a competing state (local moment, charge order, etc.) takes over as the bath-impurity coupling λ decreases. Suppression of the Kondo screening often leads to non-Fermi liquid behavior [23,24]. However, different from the quantum phase transition in bulk systems [25], at such an impurity quantum critical point, only a nonextensive term in the free energy becomes singular. It is not always straightfo...

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“…Fidelity susceptibility offers a measure for QPT in absence of any prior knowledge of order parameters [27,28]. The fidelity susceptibility F c quantifies the drastic change in the ground state of the quantum system during the phase transition, and is defined as Figure 3.…”

Section: Fidelity Susceptibilitymentioning

confidence: 99%

Quantum simulation of macro and micro quantum phase transition from paramagnetism to frustrated magnetism with a superconducting circuit

Ghosh

Sanders

2016

New J. Phys.

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We devise a scalable scheme for simulating a quantum phase transition from paramagnetism to frustrated magnetism in a superconducting flux-qubit network, and we show how to characterize this system experimentally both macroscopically and microscopically. The proposed macroscopic characterization of the quantum phase transition is based on the transition of the probability distribution for the spin-network net magnetic moment with this transition quantified by the difference between the Kullback-Leibler divergences of the distributions corresponding to the paramagnetic and frustrated magnetic phases with respect to the probability distribution at a given time during the transition. Microscopic characterization of the quantum phase transition is performed using the standard local-entanglement-witness approach. Simultaneous macro and micro characterizations of quantum phase transitions would serve to verify a quantum phase transition in two ways especially in the quantum realm for the classically intractable case of frustrated quantum magnetism.

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Fidelity Susceptibility Made Simple: A Unified Quantum Monte Carlo Approach

Cited by 86 publications

References 107 publications

Universal shift of the fidelity susceptibility peak away from the critical point of the Berezinskii-Kosterlitz-Thouless quantum phase transition

Universal shift of the fidelity susceptibility peak away from the critical point of the Berezinskii-Kosterlitz-Thouless quantum phase transition

Fidelity Susceptibility Perspective on the Kondo Effect and Impurity Quantum Phase Transitions

Quantum simulation of macro and micro quantum phase transition from paramagnetism to frustrated magnetism with a superconducting circuit

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