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arXiv:2301.11337

New critical states induced by measurement

Xinyu Sun, Hong Yao, Shao-Kai Jian

Published Jan 26, 2023• 1 citation
arXivHTMLPDF

Abstract

Finding new critical states of matter is an important subject in modern many-body physics. Here we study the effect of measurement and postselection on the critical ground state of a Luttinger liquid theory and show that it can lead to qualitatively new critical states. Depending on the Luttinger parameter $K$, the effect of measurement is irrelevant (relevant) at $K>1$ ($K<1$). We reveal that this causes an entanglement transition between two phases, one with logarithmic entanglement entropy for a subregion ($K>1$), and the other with algebraic entanglement entropy ($K<1$). At the critical point $K=1$, the measurement is marginal, and we find new critical states whose entanglement entropy exhibits a logarithmic behavior with a continuous effective central charge as a function of measurement strength. We also performed numerical density matrix renormalization group and fermionic Gaussian state simulations to support our results. We further discuss promising and feasible routes to experimentally realize new critical states in our work.

DOI
10.48550/arxiv.2301.11337

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Finding new critical states of matter is an important subject in modern many-body physics. Here we study the effect of measurement and postselection on the critical ground state of a Luttinger liquid theory and show that it can lead to qualitatively new critical states. Depending on the Luttinger parameter KKK, the effect of measurement is irrelevant (relevant) at K>1K>1K>1 (K<1K<1K<1). We reveal that this causes an entanglement transition between two phases, one with logarithmic entanglement entropy for a subregion (K>1K>1K>1), and the other with algebraic entanglement entropy (K<1K<1K<1). At the critical point K=1K=1K=1, the measurement is marginal, and we find new critical states whose entanglement entropy exhibits a logarithmic behavior with a continuous effective central charge as a function of measurement strength. We also performed numerical density matrix renormalization group and fermionic Gaussian state simulations to support our results. We further discuss promising and feasible routes to experimentally realize new critical states in our work.
We investigate entanglement phase transitions from volume-law to area-law entanglement in a quantum many-body state under continuous position measurement on the basis of the quantum trajectory approach. We find the signatures of the transitions as peak structures in the mutual information as a function of measurement strength, as previously reported for random unitary circuits with projective measurements. At the transition points, the entanglement entropy scales logarithmically and various physical quantities scale algebraically, implying emergent conformal criticality, for both integrable and nonintegrable one-dimensional interacting Hamiltonians; however, such transitions have been argued to be absent in noninteracting regimes in some previous studies. With the aid of U(1)U(1)U(1) symmetry in our model, the measurement-induced criticality exhibits a spectral signature resembling a Tomonaga-Luttinger liquid theory from symmetry-resolved entanglement. These intriguing critical phenomena are unique to steady-state regimes of the conditional dynamics at the single-trajectory level and are absent in the unconditional dynamics obeying the Lindblad master equation, in which the system ends up with the featureless, infinite-temperature mixed state. We also propose a possible experimental setup to test the predicted entanglement transition based on the subsystem particle-number fluctuations. This quantity should readily be measured by the current techniques of quantum gas microscopy and is in practice easier to obtain than the entanglement entropy itself.
Entanglement in quantum many-body systems can exhibit universal phenomena governed by long-distance properties. We study universality and phase transitions of the entanglement inherent to open many-body systems, namely, the entanglement between a system of interest and its environment. Specifically, we consider the Tomonaga-Luttinger liquid (TLL) under a local measurement and analyze its unconditioned nonunitary evolution, where the measurement outcomes are averaged over. We quantify the system-environment entanglement by the R\'enyi entropy of the post-measurement density matrix, whose size-independent term encodes the universal low-energy physics. We develop a field-theoretical description to relate the universal term to the effective ground-state degeneracy known as the ggg function in a boundary conformal field theory, and use the renormalization group method to determine its value. We show that the universal contribution is determined by the TLL parameter KKK and can exhibit singularity signifying an entanglement phase transition. Surprisingly, in certain cases the size-independent contribution can increase as a function of the measurement strength in contrast to what is na\"{\i}vely expected from the ggg-theorem. We argue that this unconventional behavior could be attributed to the dangerously irrelevant term which has been found in studies of the resistively shunted Josephson junction. We also check these results by numerical calculations in the spin-12\frac{1}{2}21​ XXZ chain subject to a site-resolved measurement. Possible experimental realization in ultracold gases, which requires no postselections, is discussed.
Local measurements can alter long-range correlations in gapless quantum matter. We propose a theory of weakly-monitored Tomonaga-Luttinger liquids, a broad class of quantum critical states in one dimension. In order to address the intrinsic randomness of the measurement record, we develop a replica instanton calculation to study Born-averaged observables. We find that when measurements are relevant, average correlators of density and phase fluctuations decay at long distances as universal power laws with logarithmic corrections, a feature we argue is peculiar to measurement-induced randomness. We characterize the full multifractal spectrum of moments of correlations functions, revealing broad, strongly non-gaussian fluctuations across the ensemble of post-measurement states. We support these analytic results with matrix-product-state calculations, and provide a general picture of measurement-altered criticality for ground states described by 1+1d conformal field theories. Our results establish that physical measurements alter critical quantum states in a manner that lies beyond both forced measurements and conventional critical scaling.
The entanglement entropy (EE) of the ground state of a one-dimensional Hamiltonian at criticality has a universal logarithmic scaling with a prefactor given by the central charge ccc of the underlying (1+1)(1+1)(1+1)-dimensional conformal field theory. When the system is probed by measurements, the entanglement in the critical ground state is inevitably affected due to wave-function collapse. In this paper, we study the effect of weak measurements on the entanglement scaling in the ground state of the one-dimensional critical transverse-field Ising model. For the measurements of the spins along their transverse spin axis, we identify interesting postmeasurement states associated with spatially uniform measurement outcomes. The EE in these states still satisfies the logarithmic scaling but with an alternative prefactor given by the effective central charge ceff{c}_{\mathrm{eff}}ceff​. We derive the analytical expression of ceff{c}_{\mathrm{eff}}ceff​ as a function of the measurement strength. With both numerical simulations and analytical studies, we show that for the EE averaged over all postmeasurement states based on their Born-rule probabilities, the effective central charge is independent of the measurement strength, contrary to the usual expectation that local and nonoverlapping measurements reduce the entanglement in the system. We also examine the behavior of the average EE under (biased) forced measurements where the measurement outcomes are sampled with a predetermined probability distribution without intersite correlations. In particular, we find an optimal probability distribution that can serve as a mean-field approximation to the Born-rule probabilities and lead to the same ceff{c}_{\mathrm{eff}}ceff​ behavior. The effects of the measurements along the longitudinal spin axis and the postmeasurement correlation functions are also discussed.
In this work, we numerically study the effect of weak measurement on deconfined quantum critical point(DQCP). Particularly, we consider the ground state of an one-dimensional spin 1/21/21/2 system with next-nearest-neighbour exchange interactions(KKK), which shows analogues phase transition to DQCP in the thermodynamic limit. This system is in the ferromagnetic phase below the critical exchange interaction KcK_cKc​ and in the valance bond solid phase above KcK_cKc​. The weak measurement is carried out by coupling a secondary ancilla system to the critical system via unitary interactions and later measuring the ancilla spins projectively. We numerically calculate entanglement entropy,correlation length, and order parameters of leading post-measurement states using uniform matrix product state representation of the quantum many-body state in the thermodynamic limit. We report asymmetric restructuring of entanglement of the post measurement states across the phase boundary under weak measurements. Especially, the trajectory (↓↓)\left(\downarrow \downarrow\right)(↓↓) describing a uniform measurement outcome given the all ancilla spins initiated in the same (↓)\left(\downarrow \right)(↓) state, shows anomalous entanglement when increasing the strength of weak measurement. The bipartite entanglement entropy strongly increases when K<KcK<K_cK<Kc​ whereas it weakly decreases when K>KcK>K_cK>Kc​. We argue with numerical evidences that observed asymmetry in entanglement would lead to a weak first order phase boundary in the thermodynamic limit. We also discuss important aspects in experimental observation of measurement induced effects linked to the strength of weak measurement and probability of post-measurement states.
Motivated by recent development of the concept of the disorder operator and its relation with entanglement entropy in bosonic systems, here we show the disorder operator successfully probes many aspects of quantum entanglement in fermionic many-body systems. From both analytical and numerical computations in free and interacting fermion systems in 1D and 2D, we find the disorder operator and the entanglement entropy exhibit similar universal scaling behavior, as a function of the boundary length of the subsystem, but with subtle yet important differences. In 1D they both follow the \log{L} log L scaling behavior with the coefficient determined by the Luttinger parameter for disorder operator, and the conformal central charge for entanglement entropy. In 2D they both show the universal L\log L L log L scaling behavior in free and interacting Fermi liquid states, with the coefficients depending on the geometry of the Fermi surfaces. However at a 2D quantum critical point with non-Fermi-liquid state, extra symmetry information is needed in the design of the disorder operator, so as to reveal the critical fluctuations as does the entanglement entropy. Our results demonstrate the fermion disorder operator can be used to probe quantum many-body entanglement related to global symmetry, and provide new tools to explore the still largely unknown territory of highly entangled fermion quantum matter in 2 or higher dimensions.