arXiv:2405.19768 · Physical review. B./Physical review. B

Measurement-induced phase transition in free bosons

Kazuki Yokomizo, Yuto Ashida

Published May 27, 2025• 6 citations

Abstract

The competition between quantum many-particle dynamics and continuous monitoring can lead to measurement-induced phase transitions (MIPTs). So far, MIPTs have been extensively explored in fermionic or spin systems. To examine the possibility of an MIPT in bosonic systems, we study the entanglement structure in continuously monitored free bosons with long-range couplings. When the measurement is local, we find that no MIPTs occur because the substantial entanglement generated by the long-range coupling overcomes the entanglement destruction due to the measurement. In contrast, we show that the nonlocal measurement can efficiently suppress the entanglement generation, leading to an MIPT where the bipartite entanglement entropy exhibits the subvolume-to-area law phase transition as the measurement strength is increased. Our numerical results indicate that the critical point should be described by a certain conformal field theory, while the transition does not belong to a conventional universality class such as Berezinskii-Kosterlitz-Thouless class.

DOI: 10.1103/y5r3-tv78

Related papers

Measurement-induced phase transitions in disordered fermions

Yunxiang Liao, Max Matheussen, Xinghai Zhang

cond-mat.stat-mechCross-listedarXiv:2605.05306May 8, 20260 citations

Entanglement Transition in a Monitored Free-Fermion Chain: From Extended Criticality to Area Law

Ori Alberton, M. Buchhold, Sebastian Diehl

arXiv:2005.09722Physical Review LettersApr 30, 2021304 citations

Free-fermion measurement-induced volume- to area-law entanglement transition in the presence of fermion interactions

Matthew S. Foster, Haoyu Guo, Chao‐Ming Jian +1 more

arXiv:2510.23706Physical review. B./Physical review. BJun 24, 20260 citations

Theory of post-selected entanglement transitions in monitored bosons

Ilia Komissarov, Emanuele G. Dalla Torre, Ahana Chakraborty

quant-pharXiv:2609.19251Sep 18, 20260 citations

Measurement-Induced Phase Transitions: Universal Entanglement Scaling at Quantum Criticality — E8 Intelligence Research

Andrew Stewart Caldin

Oct 16, 20260 citations

No measurement induced phase transition in the entanglement dynamics of monitored non-interacting one-dimensional fermions in a disordered or quasiperiodic potential

Can Yin, Bo Fan, Antonio M. García-García

quant-pharXiv:2605.10758May 12, 20260 citations

arXiv:2405.19768 · Physical review. B./Physical review. B

Measurement-induced phase transition in free bosons

Kazuki Yokomizo, Yuto Ashida

Published May 27, 2025• 6 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/y5r3-tv78

Related papers

Measurement-induced phase transitions in disordered fermions

Yunxiang Liao, Max Matheussen, Xinghai Zhang

Measurement-induced phase transitions are nonequilibrium transitions between phases characterized by distinct entanglement scaling behaviors, driven by the competition between unitary dynamics and measurements. Despite recent numerical efforts, how quenched disorder affects these transitions remains unclear. In this work, we study a $d$ -dimensional noninteracting fermionic system subject to both quenched disorder and continuous monitoring of the local particle density, and derive an effective field theory describing its long-time universal behaviors. We find that the system is governed by the same nonlinear sigma model as in the case of clean monitored fermions, with disorder entering only through a modification of model parameters. This result suggests that the presence or absence of a measurement-induced phase transition is unaffected by the introduction of disorder. In spatial dimension $d=1$ , the system exhibits only an area law phase and no transition, whereas in $d>1$ , a transition persists between an area $\times$ log law phase and an area law phase, with the critical measurement rate suppressed by disorder. Numerical simulation confirms the absence of MIPT in $d=1$ , and the linear shift of the critical measurement rate by disorder scattering rate in higher dimensions predicted by analytical theory.Measurement-induced phase transitions are nonequilibrium transitions between phases characterized by distinct entanglement scaling behaviors, driven by the competition between unitary dynamics and measurements. Despite recent numerical efforts, how quenched disorder affects these transitions remains unclear. In this work, we study a $d$-dimensional noninteracting fermionic system subject to both quenched disorder and continuous monitoring of the local particle density, and derive an effective field theory describing its long-time universal behaviors. We find that the system is governed by the same nonlinear sigma model as in the case of clean monitored fermions, with disorder entering only through a modification of model parameters. This result suggests that the presence or absence of a measurement-induced phase transition is unaffected by the introduction of disorder. In spatial dimension $d=1$, the system exhibits only an area law phase and no transition, whereas in $d>1$, a transition persists between an area$\times$log law phase and an area law phase, with the critical measurement rate suppressed by disorder. Numerical simulation confirms the absence of MIPT in $d=1$, and the linear shift of the critical measurement rate by disorder scattering rate in higher dimensions predicted by analytical theory.

cond-mat.stat-mechCross-listedarXiv:2605.05306May 8, 20260 citations

Entanglement Transition in a Monitored Free-Fermion Chain: From Extended Criticality to Area Law

Ori Alberton, M. Buchhold, Sebastian Diehl

We analyze the quantum trajectory dynamics of free fermions subject to continuous monitoring. For weak monitoring, we identify a novel dynamical regime of subextensive entanglement growth, reminiscent of a critical phase with an emergent conformal invariance. For strong monitoring, however, the dynamics favors a transition into a quantum Zeno-like area-law regime. Close to the critical point, we observe logarithmic finite size corrections, indicating a Berezinskii-Kosterlitz-Thouless mechanism underlying the transition. This uncovers an unconventional entanglement transition in an elementary, physically realistic model for weak continuous measurements. In addition, we demonstrate that the measurement aspect in the dynamics is crucial for whether or not a phase transition takes place.We analyze the quantum trajectory dynamics of free fermions subject to continuous monitoring. For weak monitoring, we identify a novel dynamical regime of subextensive entanglement growth, reminiscent of a critical phase with an emergent conformal invariance. For strong monitoring, however, the dynamics favors a transition into a quantum Zeno-like area-law regime. Close to the critical point, we observe logarithmic finite size corrections, indicating a Berezinskii-Kosterlitz-Thouless mechanism underlying the transition. This uncovers an unconventional entanglement transition in an elementary, physically realistic model for weak continuous measurements. In addition, we demonstrate that the measurement aspect in the dynamics is crucial for whether or not a phase transition takes place.

arXiv:2005.09722Physical Review LettersApr 30, 2021304 citations

Free-fermion measurement-induced volume- to area-law entanglement transition in the presence of fermion interactions

Matthew S. Foster, Haoyu Guo, Chao‐Ming Jian +1 more

At a generic volume- to area-law entanglement transition in a many-body system, quantum chaos is arrested. We argue that this tends to imply the vanishing of a certain "mass" term in the field theory of the measurement-induced phase transition (MIPT) for monitored, interacting fermions. To explore this idea, we consider the MIPT with no conserved quantities that describes 1D monitored, interacting Majorana fermions in class DIII. This is the most general problem of interacting fermions with weak fermion parity measurements. Without interactions, it is known that a noninteracting MIPT separates the area-law phase from a log-enhanced "thermal metal" phase at sufficiently weak monitoring. We conjecture that the MIPT with interactions is the same as the noninteracting one in this case; the volume-law phase arises through the dangerously irrelevant mass. The physical picture is that the mass represents a local Fermi's golden rule interparticle scattering rate density that is tantamount to the entangling rate density. The latter must vanish continuously at a continuous MIPT. On the other hand, the field theory capturing the MIPT for monitored fermions with additional continuous symmetries is expected to be different, because the interactions introduce additional terms associated to conserved Noether currents. We propose numerical tests of our conjecture. In addition, we analytically identify a candidate noninteracting critical point representing the MIPT, using a controlled $ε$ -expansion.At a generic volume- to area-law entanglement transition in a many-body system, quantum chaos is arrested. We argue that this tends to imply the vanishing of a certain "mass" term in the field theory of the measurement-induced phase transition (MIPT) for monitored, interacting fermions. To explore this idea, we consider the MIPT with no conserved quantities that describes 1D monitored, interacting Majorana fermions in class DIII. This is the most general problem of interacting fermions with weak fermion parity measurements. Without interactions, it is known that a noninteracting MIPT separates the area-law phase from a log-enhanced "thermal metal" phase at sufficiently weak monitoring. We conjecture that the MIPT with interactions is the same as the noninteracting one in this case; the volume-law phase arises through the dangerously irrelevant mass. The physical picture is that the mass represents a local Fermi's golden rule interparticle scattering rate density that is tantamount to the entangling rate density. The latter must vanish continuously at a continuous MIPT. On the other hand, the field theory capturing the MIPT for monitored fermions with additional continuous symmetries is expected to be different, because the interactions introduce additional terms associated to conserved Noether currents. We propose numerical tests of our conjecture. In addition, we analytically identify a candidate noninteracting critical point representing the MIPT, using a controlled $ε$-expansion.

arXiv:2510.23706Physical review. B./Physical review. BJun 24, 20260 citations

Theory of post-selected entanglement transitions in monitored bosons

Ilia Komissarov, Emanuele G. Dalla Torre, Ahana Chakraborty

Entanglement phase transitions driven by quantum measurements have emerged as a central paradigm in open quantum many-body physics. Such phase transitions are well established for systems with finite local Hilbert-space dimensions, such as qubits and fermions, while their realization in bosonic systems with unbounded local occupation numbers remains poorly understood. Even in the absence of interactions, number states of bosons are intrinsically non-Gaussian, preventing the use of standard correlation-matrix approaches. To address this problem, we develop a replica-free Keldysh field-theoretic framework that expresses the Renyi entropy of bosonic systems initialized in on-site Fock states in terms of permanents of matrices constructed from single-particle Green's functions. Applying this framework to a continuously monitored one-dimensional cross-stitch lattice conditioned on the no-click trajectory, we uncover a transition from volume-law to logarithmic entanglement scaling. We show that the transition is controlled by a restructuring of the non-Hermitian spectrum that changes the number of long-lived modes from extensive to finite. In the strongly monitored regime, bosons dynamically condense into a microscopic number of slowest-decaying modes, producing logarithmic entanglement scaling, whereas an extensive manifold of long-lived modes at weak monitoring gives rise to volume-law entanglement. Our results establish a distinct mechanism for measurement-induced entanglement transitions in free bosonic systems and provide a computationally efficient diagnostic of the measurement-induced bosonic condensation.Entanglement phase transitions driven by quantum measurements have emerged as a central paradigm in open quantum many-body physics. Such phase transitions are well established for systems with finite local Hilbert-space dimensions, such as qubits and fermions, while their realization in bosonic systems with unbounded local occupation numbers remains poorly understood. Even in the absence of interactions, number states of bosons are intrinsically non-Gaussian, preventing the use of standard correlation-matrix approaches. To address this problem, we develop a replica-free Keldysh field-theoretic framework that expresses the Renyi entropy of bosonic systems initialized in on-site Fock states in terms of permanents of matrices constructed from single-particle Green's functions. Applying this framework to a continuously monitored one-dimensional cross-stitch lattice conditioned on the no-click trajectory, we uncover a transition from volume-law to logarithmic entanglement scaling. We show that the transition is controlled by a restructuring of the non-Hermitian spectrum that changes the number of long-lived modes from extensive to finite. In the strongly monitored regime, bosons dynamically condense into a microscopic number of slowest-decaying modes, producing logarithmic entanglement scaling, whereas an extensive manifold of long-lived modes at weak monitoring gives rise to volume-law entanglement. Our results establish a distinct mechanism for measurement-induced entanglement transitions in free bosonic systems and provide a computationally efficient diagnostic of the measurement-induced bosonic condensation.

quant-pharXiv:2609.19251Sep 18, 20260 citations

Measurement-Induced Phase Transitions: Universal Entanglement Scaling at Quantum Criticality — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Measurement-induced phase transitions (MIPT) in quantum systems reveal a sharp entanglement phase boundary driven by the competition between unitary evolution and projective measurements, with critical points often characterized by universal exponents and effective central charges. | MATH: The MIPT is typically studied via the entanglement entropy $S = -\text{Tr}(\rho_A \ln \rho_A)$ scaling as $S \sim \frac{c}{6} \ln L$ at criticality (for 1+1D conformal field theory), where $c$ is the effective central charge. The critical measurement rate $p_c$ separates volume-law ( $S \propto L$ ) from area-law ( $S \propto \text{const}$ ) phases. For Clifford circuits, the transition is in the percolation universality class with $c = 0$ (or $c = \ln 2$ for Haar random circuits). The "1/(2π)" appears in the context of the quantum Zeno effect: for a system measured at rate $\gamma$ , the effective Hamiltonian is $H_{\text{eff}} = H - i \frac{\gamma}{2} \sum_m |m\rangle\langle Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comFINDING: Measurement-induced phase transitions (MIPT) in quantum systems reveal a sharp entanglement phase boundary driven by the competition between unitary evolution and projective measurements, with critical points often characterized by universal exponents and effective central charges. | MATH: The MIPT is typically studied via the entanglement entropy \(S = -\text{Tr}(\rho_A \ln \rho_A)$ scaling as $S \sim \frac{c}{6} \ln L$ at criticality (for 1+1D conformal field theory), where $c$ is the effective central charge. The critical measurement rate $p_c$ separates volume-law ($S \propto L$) from area-law ($S \propto \text{const}$) phases. For Clifford circuits, the transition is in the percolation universality class with $c = 0$ (or $c = \ln 2$ for Haar random circuits). The "1/(2π)" appears in the context of the quantum Zeno effect: for a system measured at rate $\gamma$, the effective Hamiltonian is \(H_{\text{eff}} = H - i \frac{\gamma}{2} \sum_m |m\rangle\langle Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Oct 16, 20260 citations

No measurement induced phase transition in the entanglement dynamics of monitored non-interacting one-dimensional fermions in a disordered or quasiperiodic potential

Can Yin, Bo Fan, Antonio M. García-García

We show that the entanglement entropy (EE) of one-dimensional (1d) non-interacting fermions with $U(1)$ symmetry in the presence of a disordered or quasi-periodic potential in which the occupation number is being monitored by homodyne or projection protocols is always in an area-law phase so no measurement induced phase transition (MIPT) occurs. The reason for the previously claimed MIPT in these systems was a finite size effect related to the fact that the maximum lattice size $L \simeq 500$ was of the order of the correlation length. By increasing the system size up to $L \simeq 18000$ , employing Graphics Processing Units (GPUs), and performing a careful finite-size scaling analysis, we find that the critical monitoring strength is consistent with zero, so no MIPT occurs. For the disordered case, these numerical results are fully supported by an analytical calculation based on mapping the problem onto a nonlinear sigma model (NLSM) that confirms the absence of the MIPT for any monitoring or disorder strength. The effect of disorder is captured by a change of symmetry from BDI to AIII, which results in an enhanced correlation length in the weak disorder limit, and by an effective monitoring strength that increases linearly with disorder.We show that the entanglement entropy (EE) of one-dimensional (1d) non-interacting fermions with $U(1)$ symmetry in the presence of a disordered or quasi-periodic potential in which the occupation number is being monitored by homodyne or projection protocols is always in an area-law phase so no measurement induced phase transition (MIPT) occurs. The reason for the previously claimed MIPT in these systems was a finite size effect related to the fact that the maximum lattice size $L \simeq 500$ was of the order of the correlation length. By increasing the system size up to $L \simeq 18000$, employing Graphics Processing Units (GPUs), and performing a careful finite-size scaling analysis, we find that the critical monitoring strength is consistent with zero, so no MIPT occurs. For the disordered case, these numerical results are fully supported by an analytical calculation based on mapping the problem onto a nonlinear sigma model (NLSM) that confirms the absence of the MIPT for any monitoring or disorder strength. The effect of disorder is captured by a change of symmetry from BDI to AIII, which results in an enhanced correlation length in the weak disorder limit, and by an effective monitoring strength that increases linearly with disorder.

quant-pharXiv:2605.10758May 12, 20260 citations

d

-dimensional noninteracting fermionic system subject to both quenched disorder and continuous monitoring of the local particle density, and derive an effective field theory describing its long-time universal behaviors. We find that the system is governed by the same nonlinear sigma model as in the case of clean monitored fermions, with disorder entering only through a modification of model parameters. This result suggests that the presence or absence of a measurement-induced phase transition is unaffected by the introduction of disorder. In spatial dimension

d=1

, the system exhibits only an area law phase and no transition, whereas in

d>1

, a transition persists between an area

\times

log law phase and an area law phase, with the critical measurement rate suppressed by disorder. Numerical simulation confirms the absence of MIPT in

d=1

, and the linear shift of the critical measurement rate by disorder scattering rate in higher dimensions predicted by analytical theory.

ε

-expansion.

S = -\text{Tr}(\rho_A \ln \rho_A)

scaling as

S \sim \frac{c}{6} \ln L

at criticality (for 1+1D conformal field theory), where

c

is the effective central charge. The critical measurement rate

p_c

separates volume-law (

S \propto L

) from area-law (

S \propto \text{const}

) phases. For Clifford circuits, the transition is in the percolation universality class with

c = 0

(or

c = \ln 2

for Haar random circuits). The "1/(2π)" appears in the context of the quantum Zeno effect: for a system measured at rate

\gamma

, the effective Hamiltonian is \(H_{\text{eff}} = H - i \frac{\gamma}{2} \sum_m |m\rangle\langle Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

We show that the entanglement entropy (EE) of one-dimensional (1d) non-interacting fermions with

U(1)

symmetry in the presence of a disordered or quasi-periodic potential in which the occupation number is being monitored by homodyne or projection protocols is always in an area-law phase so no measurement induced phase transition (MIPT) occurs. The reason for the previously claimed MIPT in these systems was a finite size effect related to the fact that the maximum lattice size

L \simeq 500

was of the order of the correlation length. By increasing the system size up to

L \simeq 18000

, employing Graphics Processing Units (GPUs), and performing a careful finite-size scaling analysis, we find that the critical monitoring strength is consistent with zero, so no MIPT occurs. For the disordered case, these numerical results are fully supported by an analytical calculation based on mapping the problem onto a nonlinear sigma model (NLSM) that confirms the absence of the MIPT for any monitoring or disorder strength. The effect of disorder is captured by a change of symmetry from BDI to AIII, which results in an enhanced correlation length in the weak disorder limit, and by an effective monitoring strength that increases linearly with disorder.